bib.bib

@book{GelMan,
    AUTHOR = {Gelfand, S. I. and Manin, Yu. I.},
     TITLE = {Homological algebra},
   EDITION = {English},
      NOTE = {Translated from the 1989 Russian original by the authors},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1999},
     PAGES = {iv+222},
      ISBN = {3-540-65378-3},
   MRCLASS = {18Gxx (14C30 14D07 18-02)},
  MRNUMBER = {1698374},
}

@misc{CTCS,
  author = {B. Milewski},
  title = {Category Theory for Programmers},
  url = {https://github.com/hmemcpy/milewski-ctfp-pdf/},
  year = {2019}
}

@book{JetNest,
    AUTHOR = {Nestruev, Jet},
     TITLE = {Smooth manifolds and observables},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {220},
   EDITION = {2},
 PUBLISHER = {Springer, Cham},
      YEAR = {2020},
     PAGES = {xviii+433},
      ISBN = {978-3-030-45650-4; 978-3-030-45649-8},
   MRCLASS = {58-01 (13Nxx 53-01 58Axx)},
  MRNUMBER = {4221224},
       DOI = {10.1007/978-3-030-45650-4},
       URL = {https://doi.org/10.1007/978-3-030-45650-4},
}

@book{Connes,
  author = {Connes and Marcolli},
  title = {Noncommutative Geometry, Quantum Fields and Motives},
}
@online{compact.proof,
  url = {https://proofwiki.org/wiki/Topological_Product_of_Compact_Spaces},
}
@online{Schuller,
  author = {F. Schuller},
  title = {Video lectures on Differential Geometry and Physics},
  url = {https://www.youtube.com/playlist?list=PLPH7f_7ZlzxTi6kS4vCmv4ZKm9u8g5yic},
}

@book{Lee,
    AUTHOR = {Lee, John M.},
     TITLE = {Introduction to smooth manifolds},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {218},
   EDITION = {2},
 PUBLISHER = {Springer, New York},
      YEAR = {2013},
     PAGES = {xvi+708},
      ISBN = {978-1-4419-9981-8},
   MRCLASS = {58-01 (53-01 57-01)},
  MRNUMBER = {2954043},
}

@book {LeeTop,
    AUTHOR = {Lee, John M.},
     TITLE = {Introduction to topological manifolds},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {202},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {2000},
     PAGES = {xviii+385},
      ISBN = {0-387-98759-2; 0-387-95026-5},
   MRCLASS = {57-01 (54-01 55-01)},
  MRNUMBER = {1759845},
MRREVIEWER = {Boris\ N.\ Apanasov},
}

@book{Gadea,
    AUTHOR = {Gadea, Pedro M. and Mu\~noz Masqu\'e, Jaime and Mykytyuk, Ihor
              V.},
     TITLE = {Analysis and algebra on differentiable manifolds},
    SERIES = {Problem Books in Mathematics},
   EDITION = {2},
 PUBLISHER = {Springer, London},
      YEAR = {2013},
     PAGES = {xxvi+617},
      ISBN = {978-94-007-5951-0; 978-94-007-5952-7},
   MRCLASS = {58-01 (53-01 58Axx)},
  MRNUMBER = {3014453},
       DOI = {10.1007/978-94-007-5952-7},
       URL = {https://doi.org/10.1007/978-94-007-5952-7},
}

@book{LieRiem,
    AUTHOR = {Lee, John M.},
     TITLE = {Riemannian manifolds},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {176},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1997},
     PAGES = {xvi+224},
      ISBN = {0-387-98271-X},
   MRCLASS = {53-01 (53C21)},
  MRNUMBER = {1468735},
MRREVIEWER = {Man\ Chun\ Leung},
       DOI = {10.1007/b98852},
       URL = {https://doi.org/10.1007/b98852},
}

@book{Jost,
    AUTHOR = {Jost, J\"urgen},
     TITLE = {Riemannian geometry and geometric analysis},
    SERIES = {Universitext},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1995},
     PAGES = {xii+401},
      ISBN = {3-540-57113-2},
   MRCLASS = {53C21 (53-01 53C20 58-01 58E05 58E10)},
  MRNUMBER = {1351009},
MRREVIEWER = {Man\ Chun\ Leung},
       DOI = {10.1007/978-3-662-03118-6},
       URL = {https://doi.org/10.1007/978-3-662-03118-6},
}

@online{smooth.structures,
  url = {https://mathoverflow.net/questions/47569/what-makes-four-dimensions-special},
}

@misc{Aguilar,
  title = {{F}iber {B}undles},
  url = {https://paginas.matem.unam.mx/cprieto/phocadownloadpap/fiber},
  author = {Marcelo A. Aguilar and Carlos Prieto},
  year = {2010}
}

@book{Dundas,
  author = {Bj{\o}rn Ian Dundas},
  title = {Differential Topology},
  year = {2013},
  url = {https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=0603e3854c4dc13a2a283072ef834b05e8eec607},
}

@online{hopf,
  url = {https://www.youtube.com/watch?v=AKotMPGFJYk},
}

@book{RS1,
    AUTHOR = {Rudolph, Gerd and Schmidt, Matthias},
     TITLE = {Differential geometry and mathematical physics. {P}art {I}},
    SERIES = {Theoretical and Mathematical Physics},
 PUBLISHER = {Springer, Dordrecht},
      YEAR = {2013},
     PAGES = {xiv+759},
      ISBN = {978-94-007-5344-0; 978-94-007-5345-7},
   MRCLASS = {58-02 (53-02)},
  MRNUMBER = {3012162},
MRREVIEWER = {Tomasz\ Rybicki},
       DOI = {10.1007/978-94-007-5345-7},
       URL = {https://doi.org/10.1007/978-94-007-5345-7},
}

@book{RS2,
    AUTHOR = {Rudolph, Gerd and Schmidt, Matthias},
     TITLE = {Differential geometry and mathematical physics. {P}art {II}},
    SERIES = {Theoretical and Mathematical Physics},
 PUBLISHER = {Springer, Dordrecht},
      YEAR = {2017},
     PAGES = {xv+830},
      ISBN = {978-94-024-0958-1; 978-94-024-0959-8},
   MRCLASS = {58-02 (53-02 53Z05 58Z05)},
  MRNUMBER = {3616138},
MRREVIEWER = {Tomasz\ Rybicki},
       DOI = {10.1007/978-94-024-0959-8},
       URL = {https://doi.org/10.1007/978-94-024-0959-8},
}

@article{Atiyah,
    AUTHOR = {Atiyah, M. F.},
     TITLE = {Vector bundles over an elliptic curve},
   JOURNAL = {Proc. London Math. Soc. (3)},
  FJOURNAL = {Proceedings of the London Mathematical Society. Third Series},
    VOLUME = {7},
      YEAR = {1957},
     PAGES = {414--452},
      ISSN = {0024-6115,1460-244X},
   MRCLASS = {14.55 (14.20)},
  MRNUMBER = {131423},
MRREVIEWER = {F.\ Hirzebruch},
       DOI = {10.1112/plms/s3-7.1.414},
       URL = {https://doi.org/10.1112/plms/s3-7.1.414},
}

@book{Bredon,
    AUTHOR = {Bredon, Glen E.},
     TITLE = {Topology and geometry},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {139},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1993},
     PAGES = {xiv+557},
      ISBN = {0-387-97926-3},
   MRCLASS = {55-01 (54-01 57-01)},
  MRNUMBER = {1224675},
MRREVIEWER = {Donald\ W.\ Kahn},
       DOI = {10.1007/978-1-4757-6848-0},
       URL = {https://doi.org/10.1007/978-1-4757-6848-0},
}

@book{Milnor,
    AUTHOR = {Milnor, J.},
     TITLE = {Morse theory},
    SERIES = {Annals of Mathematics Studies},
    VOLUME = {No. 51},
 PUBLISHER = {Princeton University Press, Princeton, NJ},
      YEAR = {1963},
     PAGES = {vi+153},
   MRCLASS = {57.50 (53.72)},
  MRNUMBER = {163331},
MRREVIEWER = {H.\ I.\ Levine},
}

@book{Munk,
    AUTHOR = {Munkres, James R.},
     TITLE = {Topology},
   EDITION = {2},
 PUBLISHER = {Prentice Hall, Inc., Upper Saddle River, NJ},
      YEAR = {2000},
     PAGES = {xvi+537},
      ISBN = {0-13-181629-2},
   MRCLASS = {54-01},
  MRNUMBER = {3728284},
}

@book{Hatcher,
    AUTHOR = {Hatcher, Allen},
     TITLE = {Algebraic topology},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2002},
     PAGES = {xii+544},
      ISBN = {0-521-79160-X; 0-521-79540-0},
   MRCLASS = {55-01 (55-00)},
  MRNUMBER = {1867354},
MRREVIEWER = {Donald\ W.\ Kahn},
}


@misc{HatcherVB,
  author = {A. Hatcher},
  title = {Vector Bundles and K-Theory},
  url = {https://pi.math.cornell.edu/~hatcher/VBKT/VB.pdf},
  year = {2017}
}

@book {Huybrechts,
    AUTHOR = {Huybrechts, Daniel},
     TITLE = {Complex geometry},
    SERIES = {Universitext},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2005},
     PAGES = {xii+309},
      ISBN = {3-540-21290-6},
   MRCLASS = {32Qxx (14-01 32-01 32G05 32J25 53C55 53C56)},
  MRNUMBER = {2093043},
MRREVIEWER = {Richard\ P.\ Thomas},
}

@book{BottTu,
    AUTHOR = {Bott, Raoul and Tu, Loring W.},
     TITLE = {Differential forms in algebraic topology},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {82},
 PUBLISHER = {Springer-Verlag, New York-Berlin},
      YEAR = {1982},
     PAGES = {xiv+331},
      ISBN = {0-387-90613-4},
   MRCLASS = {57R19 (55-02 58-01 58A12)},
  MRNUMBER = {658304},
MRREVIEWER = {Hansklaus\ Rummler},
}

@book{tomDieck,
    AUTHOR = {tom Dieck, Tammo},
     TITLE = {Algebraic topology},
    SERIES = {EMS Textbooks in Mathematics},
 PUBLISHER = {European Mathematical Society (EMS), Z\"urich},
      YEAR = {2008},
     PAGES = {xii+567},
      ISBN = {978-3-03719-048-7},
   MRCLASS = {55-01},
  MRNUMBER = {2456045},
MRREVIEWER = {Donald\ M.\ Davis},
       DOI = {10.4171/048},
       URL = {https://doi.org/10.4171/048},
}

@book{Rotman,
    AUTHOR = {Rotman, Joseph J.},
     TITLE = {An introduction to homological algebra},
    SERIES = {Universitext},
   EDITION = {2},
 PUBLISHER = {Springer, New York},
      YEAR = {2009},
     PAGES = {xiv+709},
      ISBN = {978-0-387-24527-0},
   MRCLASS = {18Gxx (13Dxx 16Exx 18-01 20J06)},
  MRNUMBER = {2455920},
MRREVIEWER = {Fernando\ Muro},
       DOI = {10.1007/b98977},
       URL = {https://doi.org/10.1007/b98977},
}

@book{Bergman,
    AUTHOR = {Bergman, George M.},
     TITLE = {An invitation to general algebra and universal constructions},
    SERIES = {Universitext},
   EDITION = {2},
 PUBLISHER = {Springer, Cham},
      YEAR = {2015},
     PAGES = {x+572},
      ISBN = {978-3-319-11477-4; 978-3-319-11478-1},
   MRCLASS = {08-01 (00A05 18Axx 20Fxx)},
  MRNUMBER = {3309721},
       DOI = {10.1007/978-3-319-11478-1},
       URL = {https://math.berkeley.edu/~gbergman/245/},
}


@book{Leinster,
    AUTHOR = {Leinster, Tom},
     TITLE = {Basic category theory},
    SERIES = {Cambridge Studies in Advanced Mathematics},
    VOLUME = {143},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2014},
     PAGES = {viii+183},
      ISBN = {978-1-107-04424-1},
   MRCLASS = {18-01},
  MRNUMBER = {3307165},
MRREVIEWER = {Philippe\ Gaucher},
       DOI = {10.1017/CBO9781107360068},
       URL = {https://doi.org/10.1017/CBO9781107360068},
    eprint = {https://arxiv.org/abs/1612.09375},
}

@misc{Perrone,
  author = {P. Perrone},
  title = {Notes on Category Theory with examples from basic mathematics},
  year = {2019},
  eprint = {https://arxiv.org/abs/1912.10642},
}

@book{May,
    AUTHOR = {May, J. P.},
     TITLE = {A concise course in algebraic topology},
    SERIES = {Chicago Lectures in Mathematics},
 PUBLISHER = {University of Chicago Press, Chicago, IL},
      YEAR = {1999},
     PAGES = {x+243},
      ISBN = {0-226-51182-0; 0-226-51183-9},
   MRCLASS = {55-02 (18-02 57-02)},
  MRNUMBER = {1702278},
MRREVIEWER = {R.\ M.\ Vogt},
  eprint = {https://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf},
}


@book{Spanier,
    AUTHOR = {Spanier, Edwin H.},
     TITLE = {Algebraic topology},
 PUBLISHER = {McGraw-Hill Book Co., New York-Toronto-London},
      YEAR = {1966},
     PAGES = {xiv+528},
   MRCLASS = {55.00},
  MRNUMBER = {210112},
MRREVIEWER = {S.-T.\ Hu},
}

@book{DK,
    AUTHOR = {Duistermaat, J. J. and Kolk, J. A. C.},
     TITLE = {Lie groups},
    SERIES = {Universitext},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2000},
     PAGES = {viii+344},
      ISBN = {3-540-15293-8},
   MRCLASS = {22Exx (22-01 22C05 43-01)},
  MRNUMBER = {1738431},
MRREVIEWER = {Aloysius\ Helminck},
       DOI = {10.1007/978-3-642-56936-4},
       URL = {https://doi.org/10.1007/978-3-642-56936-4},
}

@misc{Neeb,
  author = {K. H. Neeb},
  title = {Infinite-Dimensional Lie Groups},
  year = {2009},
  eprint = {https://cel.hal.science/cel-00391789},
}
@book{Warner,
    AUTHOR = {Warner, Frank W.},
     TITLE = {Foundations of differentiable manifolds and {L}ie groups},
 PUBLISHER = {Scott, Foresman \& Co., Glenview, Ill.-London},
      YEAR = {1971},
     PAGES = {viii+270},
   MRCLASS = {58A05 (22E15)},
  MRNUMBER = {295244},
MRREVIEWER = {N.\ J.\ Hicks},
}

@book{Onishchik,
  author="Onishchik, A. L.",
  editor="Onishchik, A. L.",
  title="Lie Groups and Lie Algebras I: Foundations of Lie Theory Lie Transformation Groups",
  year="1993",
  publisher="Springer Berlin Heidelberg",
  address="Berlin, Heidelberg",
  isbn="978-3-642-57999-8",
  doi="10.1007/978-3-642-57999-8_10",
  url="https://doi.org/10.1007/978-3-642-57999-8_10"
}

@book{Sepanski,
    AUTHOR = {Sepanski, Mark R.},
     TITLE = {Compact {L}ie groups},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {235},
 PUBLISHER = {Springer, New York},
      YEAR = {2007},
     PAGES = {xiv+198},
      ISBN = {978-0-387-30263-8; 0-387-30263-8},
   MRCLASS = {22Exx},
  MRNUMBER = {2279709},
MRREVIEWER = {David\ A.\ Renard},
       DOI = {10.1007/978-0-387-49158-5},
       URL = {https://doi.org/10.1007/978-0-387-49158-5},
}


@book{Munkres,
    AUTHOR = {Munkres, James R.},
     TITLE = {Elements of algebraic topology},
 PUBLISHER = {Addison-Wesley Publishing Company, Menlo Park, CA},
      YEAR = {1984},
     PAGES = {ix+454},
      ISBN = {0-201-04586-9},
   MRCLASS = {55-01},
  MRNUMBER = {755006},
MRREVIEWER = {Christopher\ W.\ Stark},
}

@book{Shastri,
    AUTHOR = {Shastri, Anant R.},
     TITLE = {Basic algebraic topology},
 PUBLISHER = {CRC Press, Boca Raton, FL},
      YEAR = {2014},
     PAGES = {xvi+535},
      ISBN = {978-1-4665-6243-1},
   MRCLASS = {55-01},
  MRNUMBER = {3134904},
MRREVIEWER = {Fabio\ Ferrari Ruffino},
}

@book{HN,
    AUTHOR = {Hilgert, Joachim and Neeb, Karl-Hermann},
     TITLE = {Structure and geometry of {L}ie groups},
    SERIES = {Springer Monographs in Mathematics},
 PUBLISHER = {Springer, New York},
      YEAR = {2012},
     PAGES = {x+744},
      ISBN = {978-0-387-84793-1; 978-0-387-84794-8},
   MRCLASS = {22-02 (22-01)},
  MRNUMBER = {3025417},
MRREVIEWER = {K.\ Strambach},
       DOI = {10.1007/978-0-387-84794-8},
       URL = {https://doi.org/10.1007/978-0-387-84794-8},
}

@book{Sharpe,
    AUTHOR = {Sharpe, R. W.},
     TITLE = {Differential geometry: Cartan's generalization of Klein's Erlangen program},
    SERIES = {Graduate Texts in Mathematics},
    VOLUME = {166},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1997},
     PAGES = {xx+421},
      ISBN = {0-387-94732-9},
   MRCLASS = {53Cxx (53-02)},
  MRNUMBER = {1453120},
MRREVIEWER = {William\ Goldman},
}

@book{Cap,
    AUTHOR = {\v Cap, Andreas and Slov\'ak, Jan},
     TITLE = {Parabolic geometries},
    SERIES = {Mathematical Surveys and Monographs},
    VOLUME = {154},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2009},
     PAGES = {x+628},
      ISBN = {978-0-8218-2681-2},
   MRCLASS = {53C10 (17B60 22E60 53A55 53C30 58J70)},
  MRNUMBER = {2532439},
MRREVIEWER = {Stuart\ Armstrong},
       DOI = {10.1090/surv/154},
       URL = {https://doi.org/10.1090/surv/154},
}

@book{Kolar,
    AUTHOR = {Kol\'a\v r, Ivan and Michor, Peter W. and Slov\'ak, Jan},
     TITLE = {Natural operations in differential geometry},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {1993},
     PAGES = {vi+434},
      ISBN = {3-540-56235-4},
   MRCLASS = {58A20 (53A55 53B05 53C05)},
  MRNUMBER = {1202431},
MRREVIEWER = {Jaime\ Mu\~noz Masqu\'e},
       DOI = {10.1007/978-3-662-02950-3},
       URL = {https://doi.org/10.1007/978-3-662-02950-3},
}

@misc{Vakar,
      title={Principal Bundles and Gauge Theories}, 
      author={Matthijs V\'ak\'ar},
      year={2021},
      eprint={2110.06334},
      archivePrefix={arXiv},
      primaryClass={math-ph},
      url={https://arxiv.org/abs/2110.06334}, 
}

@article{Hoyo,
    AUTHOR = {del Hoyo, Matias},
     TITLE = {Complete connections on fiber bundles},
   JOURNAL = {Indag. Math. (N.S.)},
  FJOURNAL = {Koninklijke Nederlandse Akademie van Wetenschappen.
              Indagationes Mathematicae. New Series},
    VOLUME = {27},
      YEAR = {2016},
    NUMBER = {4},
     PAGES = {985--990},
      ISSN = {0019-3577,1872-6100},
   MRCLASS = {53C05},
  MRNUMBER = {3542951},
MRREVIEWER = {Lorenz\ J.\ Schwachh\"ofer},
       DOI = {10.1016/j.indag.2016.06.009},
       URL = {https://doi.org/10.1016/j.indag.2016.06.009},
    eprint = {https://arxiv.org/abs/1512.03847},
}

@book{Kobayashi,
    AUTHOR = {Kobayashi, Shoshichi},
     TITLE = {Differential geometry of complex vector bundles},
    SERIES = {Princeton Legacy Library},
 PUBLISHER = {Princeton University Press, Princeton, NJ},
      YEAR = {2014},
     PAGES = {xi + 304},
      ISBN = {978-0-691-60329-2},
   MRCLASS = {53C55 (01A75 32-02 32L05 32L10 32L20)},
  MRNUMBER = {3643615},
}

@book{Spivak2,
  author = {M. Spivak},
  title = {A comprehensive introduction to differential geometry},
  year = {1999},
  edition = {3},
  volume = {2},
}

@book{Spivak3,
  author = {M. Spivak},
  title = {A comprehensive introduction to differential geometry},
  year = {1999},
  edition = {3},
  volume = {3},
}

@article{OFarrill,
  author = {J. Figueroa-O'Farrill},
  title = {On the intrinsic torsion of spacetime structures},
  year = {2020},
  eprint = {https://arxiv.org/abs/2009.01948v1},
}

@article{Laquer,
    AUTHOR = {Laquer, H. Turner},
     TITLE = {Invariant affine connections on {L}ie groups},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {331},
      YEAR = {1992},
    NUMBER = {2},
     PAGES = {541--551},
      ISSN = {0002-9947,1088-6850},
   MRCLASS = {53C05 (22E30 53C30)},
  MRNUMBER = {1075384},
       DOI = {10.2307/2154126},
       URL = {https://doi.org/10.2307/2154126},
}

@book{Marsden,
    AUTHOR = {Abraham, Ralph and Marsden, Jerrold E.},
     TITLE = {Foundations of mechanics},
   EDITION = {2},
 PUBLISHER = {Benjamin/Cummings Publishing Co., Inc., Advanced Book Program,
              Reading, MA},
      YEAR = {1978},
     PAGES = {xxii+m-xvi+806},
      ISBN = {0-8053-0102-X},
   MRCLASS = {58Fxx (70-02 70F07)},
  MRNUMBER = {515141},
MRREVIEWER = {D.\ L.\ Rod},
}

@book{Bryant,
    AUTHOR = {Bryant, R. L. and Chern, S. S. and Gardner, R. B. and
              Goldschmidt, H. L. and Griffiths, P. A.},
     TITLE = {Exterior differential systems},
    SERIES = {Mathematical Sciences Research Institute Publications},
    VOLUME = {18},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {1991},
     PAGES = {viii+475},
      ISBN = {0-387-97411-3},
   MRCLASS = {58A15 (35N10 58-01 58-02 58A17 58G05)},
  MRNUMBER = {1083148},
MRREVIEWER = {Irl\ Bivens},
       DOI = {10.1007/978-1-4613-9714-4},
       URL = {https://doi.org/10.1007/978-1-4613-9714-4},
}

@book {Ivey,
    AUTHOR = {Ivey, Thomas A. and Landsberg, J. M.},
     TITLE = {Cartan for beginners: differential geometry via moving frames
              and exterior differential systems},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {61},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {2003},
     PAGES = {xiv+378},
      ISBN = {0-8218-3375-8},
   MRCLASS = {53-01 (58A15)},
  MRNUMBER = {2003610},
MRREVIEWER = {Emilio\ Musso},
       DOI = {10.1090/gsm/061},
       URL = {https://doi.org/10.1090/gsm/061},
}

@book{Olver,
    AUTHOR = {Olver, Peter J.},
     TITLE = {Applications of {L}ie groups to differential equations},
    SERIES = {Lecture Notes},
 PUBLISHER = {Oxford University, Mathematical Institute, Oxford},
      YEAR = {1980},
     PAGES = {vi+170},
   MRCLASS = {58F35 (22E15 34A99 35A30 58-01)},
  MRNUMBER = {673378},
}

@book{doCarmo,
    AUTHOR = {do Carmo, Manfredo P.},
     TITLE = {Differential geometry of curves \& surfaces},
   EDITION = {2},
 PUBLISHER = {Dover Publications, Inc., Mineola, NY},
      YEAR = {2016},
     PAGES = {xvi+510},
      ISBN = {978-0-486-80699-0; 0-486-80699-5},
   MRCLASS = {53-01 (53A04 53A05)},
  MRNUMBER = {3837152},
}

@book{Berline,
    AUTHOR = {Berline, Nicole and Getzler, Ezra and Vergne, Mich\`ele},
     TITLE = {Heat kernels and {D}irac operators},
    SERIES = {Grundlehren Text Editions},
 PUBLISHER = {Springer-Verlag, Berlin},
      YEAR = {2004},
     PAGES = {x+363},
      ISBN = {3-540-20062-2},
   MRCLASS = {58J35 (35K05 35Q40 47G30 58J60)},
  MRNUMBER = {2273508},
}

@misc{schreiber,
      title={Parallel Transport and Functors}, 
      author={Urs Schreiber and Konrad Waldorf},
      year={2014},
      eprint={0705.0452},
      archivePrefix={arXiv},
      primaryClass={id='math.DG' full_name='Differential Geometry' is_active=True alt_name='dg-ga' in_archive='math' is_general=False description='Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis'},
      doi={10.48550/arXiv.0705.0452}
}

@misc{deift,
      title={Fifty Years of KdV: An Integrable System}, 
      author={Percy Deift},
      year={2019},
      eprint={1902.10267},
      archivePrefix={arXiv},
      primaryClass={id='math-ph'}
}

@book{moser,
    AUTHOR = {H\'elein, Fr\'ed\'eric},
     TITLE = {Constant mean curvature surfaces, harmonic maps and integrable
              systems},
    SERIES = {Lectures in Mathematics ETH Z\"urich},
      NOTE = {Notes taken by Roger Moser},
 PUBLISHER = {Birkh\"auser Verlag, Basel},
      YEAR = {2001},
     PAGES = {122},
      ISBN = {3-7643-6576-5},
   MRCLASS = {53A10 (37K25 53C43 58E20)},
  MRNUMBER = {1844305},
MRREVIEWER = {Pascal\ S.\ Romon},
       DOI = {10.1007/978-3-0348-8330-6},
       URL = {https://doi.org/10.1007/978-3-0348-8330-6},
}

@book{babelon,
    AUTHOR = {Babelon, Olivier and Bernard, Denis and Talon, Michel},
     TITLE = {Introduction to classical integrable systems},
    SERIES = {Cambridge Monographs on Mathematical Physics},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2003},
     PAGES = {xii+602},
      ISBN = {0-521-82267-X},
   MRCLASS = {37J35 (35Q51 35Q53 37K10 37K15 37K20 70H06)},
  MRNUMBER = {1995460},
MRREVIEWER = {Fritz\ Gesztesy},
       DOI = {10.1017/CBO9780511535024},
       URL = {https://doi.org/10.1017/CBO9780511535024},
}

@book{cartan45,
    AUTHOR = {Cartan, \'Elie},
     TITLE = {Les syst\`emes diff\'erentiels ext\'erieurs et leurs
              applications g\'eom\'etriques},
    SERIES = {Actualit\'es Scientifiques et Industrielles},
    VOLUME = {No. 994},
 PUBLISHER = {Hermann \& Cie, Paris},
      YEAR = {1945},
     PAGES = {214},
   MRCLASS = {36.0X},
  MRNUMBER = {16174},
MRREVIEWER = {J.\ A.\ Schouten},
}

@misc{McKayCartan,
      title={An introduction to Cartan geometries}, 
      author={Benjamin McKay},
      year={2024},
      eprint={2302.14457},
      archivePrefix={arXiv},
      primaryClass={math.DG},
      url={https://arxiv.org/abs/2302.14457v21}, 
}

@misc{McKayEDS,
      title={Introduction to exterior differential systems}, 
      author={Benjamin McKay},
      year={2020},
      eprint={1706.09697},
      archivePrefix={arXiv},
      primaryClass={math.DG},
      url={https://arxiv.org/abs/1706.09697}, 
}

@book{Borcherds,
     title={Berkeley Lectures on Lie Groups and Quantum Groups},
     author={Richard Borcherds and Mark Haiman and Theo Johnson-Freyd and Nicolai Reshetikhin and Vera Serganova},
     year={2024},
     url={http://categorified.net/LieQuantumGroups.pdf},
}

@book{Goldman,
    AUTHOR = {Goldman, William M.},
     TITLE = {Geometric structures on manifolds},
    SERIES = {Graduate Studies in Mathematics},
    VOLUME = {227},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {[2022] \copyright 2022},
     PAGES = {li+409},
      ISBN = {[9781470471033]; [9781470471989]; [9781470471972]},
   MRCLASS = {57-01 (22Exx 53-01)},
  MRNUMBER = {4500072},
MRREVIEWER = {Michel\ Nguiffo B. Boyom},
       DOI = {10.1090/gsm/227},
       URL = {https://doi.org/10.1090/gsm/227},
}

@article{Dieudonne,
    AUTHOR = {Dieudonn\'e, Jean},
     TITLE = {Sur une g\'en\'eralisation du groupe orthogonal \`a{} quatre
              variables},
   JOURNAL = {Arch. Math.},
  FJOURNAL = {Archiv der Mathematik},
    VOLUME = {1},
      YEAR = {1949},
     PAGES = {282--287},
      ISSN = {0003-889X,1420-8938},
   MRCLASS = {09.0X},
  MRNUMBER = {29360},
MRREVIEWER = {L.\ K.\ Hua},
       DOI = {10.1007/BF02038756},
       URL = {https://doi.org/10.1007/BF02038756},
}

@article{Matveev,
    AUTHOR = {Matveev, Vladimir S. and Troyanov, Marc},
     TITLE = {Completeness and incompleteness of the {B}inet-{L}egendre
              metric},
   JOURNAL = {Eur. J. Math.},
  FJOURNAL = {European Journal of Mathematics},
    VOLUME = {1},
      YEAR = {2015},
    NUMBER = {3},
     PAGES = {483--502},
      ISSN = {2199-675X,2199-6768},
   MRCLASS = {53B40 (53C60)},
  MRNUMBER = {3401902},
MRREVIEWER = {Akbar\ Tayebi},
       DOI = {10.1007/s40879-015-0046-4},
       URL = {https://doi.org/10.1007/s40879-015-0046-4},
}

@article{Melnick,
    AUTHOR = {Melnick, Karin},
     TITLE = {A {F}robenius theorem for {C}artan geometries, with
              applications},
   JOURNAL = {Enseign. Math. (2)},
  FJOURNAL = {L'Enseignement Math\'ematique. Revue Internationale. 2e
              S\'erie},
    VOLUME = {57},
      YEAR = {2011},
    NUMBER = {1-2},
     PAGES = {57--89},
      ISSN = {0013-8584},
   MRCLASS = {53C30 (53C05 57S15 57S20)},
  MRNUMBER = {2850584},
MRREVIEWER = {Andreas\ Cap},
       DOI = {10.4171/LEM/57-1-3},
       URL = {https://doi.org/10.4171/LEM/57-1-3},
}

@book{Shima,
    AUTHOR = {Shima, Hirohiko},
     TITLE = {The geometry of {H}essian structures},
 PUBLISHER = {World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ},
      YEAR = {2007},
     PAGES = {xiv+246},
      ISBN = {978-981-270-031-5; 981-270-031-5},
   MRCLASS = {53A15 (53-02)},
  MRNUMBER = {2293045},
MRREVIEWER = {John\ C.\ Loftin},
       DOI = {10.1142/9789812707536},
       URL = {https://doi.org/10.1142/9789812707536},
}

@article {Shima95,
    AUTHOR = {Shima, Hirohiko and Yagi, Katsumi},
     TITLE = {Geometry of {H}essian manifolds},
   JOURNAL = {Differential Geom. Appl.},
  FJOURNAL = {Differential Geometry and its Applications},
    VOLUME = {7},
      YEAR = {1997},
    NUMBER = {3},
     PAGES = {277--290},
      ISSN = {0926-2245,1872-6984},
   MRCLASS = {53A15 (53C20)},
  MRNUMBER = {1480540},
MRREVIEWER = {William\ Goldman},
       DOI = {10.1016/S0926-2245(96)00057-5},
       URL = {https://doi.org/10.1016/S0926-2245(96)00057-5},
}

@book{Mimura,
    AUTHOR = {Mimura, Mamoru and Toda, Hirosi},
     TITLE = {Topology of {L}ie groups. {I}, {II}},
    SERIES = {Translations of Mathematical Monographs},
    VOLUME = {91},
   EDITION = {Japanese},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {1991},
     PAGES = {iv+451},
      ISBN = {0-8218-4541-1},
   MRCLASS = {55-02 (22-02 55P99 57T20 57T25)},
  MRNUMBER = {1122592},
MRREVIEWER = {V.\ P.\ Snaith},
       DOI = {10.1090/mmono/091},
       URL = {https://doi.org/10.1090/mmono/091},
}

@book{OlverEquiv,
    AUTHOR = {Olver, Peter J.},
     TITLE = {Equivalence, invariants, and symmetry},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {1995},
     PAGES = {xvi+525},
      ISBN = {0-521-47811-1},
   MRCLASS = {58A15 (22E15 35A30 58-02 58A17 58A20 58E40 58F36)},
  MRNUMBER = {1337276},
MRREVIEWER = {Jaime\ Mu\~noz Masqu\'e},
       DOI = {10.1017/CBO9780511609565},
       URL = {https://doi.org/10.1017/CBO9780511609565},
}

@book{Kras,
    AUTHOR = {Bocharov, A. V. and Chetverikov, V. N. and Duzhin, S. V. and
              Khor'kova, N. G. and Krasil'shchik, I. S. and
              Samokhin, A. V. and Torkhov, Yu.\ N. and Verbovetsky, A. M.
              and Vinogradov, A. M.},
     TITLE = {Symmetries and conservation laws for differential equations of
              mathematical physics},
    SERIES = {Translations of Mathematical Monographs},
    VOLUME = {182},
      NOTE = {Edited and with a preface by Krasil'shchik and
              Vinogradov,
              Translated from the 1997 Russian original by Verbovetsky and Krasil'shchik},
 PUBLISHER = {American Mathematical Society, Providence, RI},
      YEAR = {1999},
     PAGES = {xiv+333},
      ISBN = {0-8218-0958-X},
   MRCLASS = {58J70 (34C14 35A30 35L65 37K10 37K35 58A20 58J72)},
  MRNUMBER = {1670044},
MRREVIEWER = {Juha\ Pohjanpelto},
       DOI = {10.1090/mmono/182},
       URL = {https://doi.org/10.1090/mmono/182},
}

@book{Hydon,
    AUTHOR = {Hydon, Peter E.},
     TITLE = {Symmetry methods for differential equations},
    SERIES = {Cambridge Texts in Applied Mathematics},
      NOTE = {A beginner's guide},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2000},
     PAGES = {xii+213},
      ISBN = {0-521-49703-5; 0-521-49786-8},
   MRCLASS = {58J70 (34A25 34A26 34C14 35-01 35A30)},
  MRNUMBER = {1741548},
MRREVIEWER = {Mark\ E.\ Fels},
       DOI = {10.1017/CBO9780511623967},
       URL = {https://doi.org/10.1017/CBO9780511623967},
}

@book{Bluman,
    AUTHOR = {Bluman, George W. and Anco, Stephen C.},
     TITLE = {Symmetry and integration methods for differential equations},
    SERIES = {Applied Mathematical Sciences},
    VOLUME = {154},
 PUBLISHER = {Springer-Verlag, New York},
      YEAR = {2002},
     PAGES = {x+419},
      ISBN = {0-387-98654-5},
   MRCLASS = {34C14 (35A22 35A30 58J70)},
  MRNUMBER = {1914342},
MRREVIEWER = {Mark\ E.\ Fels},
}

@misc{Gungor,
      title={Notes on Lie symmetry group methods for differential equations}, 
      author={F. Güngör},
      year={2024},
      eprint={1901.01543},
      archivePrefix={arXiv},
      primaryClass={math.CA},
      url={https://arxiv.org/abs/1901.01543}, 
}

@book{Weyl,
    AUTHOR = {Weyl, Hermann},
     TITLE = {The {C}lassical {G}roups. {T}heir {I}nvariants and
              {R}epresentations},
 PUBLISHER = {Princeton University Press, Princeton, NJ},
      YEAR = {1939},
     PAGES = {xii+302},
   MRCLASS = {20.0X},
  MRNUMBER = {255},
MRREVIEWER = {C.\ Chevalley},
}