references.bib

@book{Renteln_2013, 
  place={Cambridge}, 
  title={Manifolds, Tensors, and Forms: An Introduction for Mathematicians and Physicists}, 
  publisher={Cambridge University Press}, 
  author={Renteln, Paul}, 
  year={2013}
}

@book{lee2000introduction,
  title={Introduction to Topological Manifolds},
  author={Lee, J.M.},
  isbn={9780387987590},
  lccn={00026156},
  series={Graduate texts in mathematics},
  url={https://books.google.ae/books?id=OP758-XpU3MC},
  year={2000},
  publisher={Springer}
}

@book{lee2003introduction,
  title={Introduction to Smooth Manifolds},
  author={Lee, J.M.},
  isbn={9780387954486},
  lccn={2002070454},
  series={Graduate Texts in Mathematics},
  url={https://books.google.ae/books?id=eqfgZtjQceYC},
  year={2003},
  publisher={Springer}
}

@misc{GnL,
  author       = {F P Schuller},
  howpublished = {gravity-and-light.org},
  title        = {WE-Heraeus International Winter School on Gravity and Light, Linz, Austria},
  year         = {2015}
}

@book{axler2014linear,
  title={Linear Algebra Done Right},
  author={Axler, S.},
  isbn={9783319110806},
  series={Undergraduate Texts in Mathematics},
  url={https://books.google.ae/books?id=5qYxBQAAQBAJ},
  year={2014},
  publisher={Springer International Publishing}
}

@book{johnston2021introduction,
  title={Introduction to Linear and Matrix Algebra},
  author={Johnston, N.},
  isbn={9783030528119},
  url={https://books.google.ae/books?id=y24vEAAAQBAJ},
  year={2021},
  publisher={Springer International Publishing}
}

@book{johnston2021advanced,
  title={Advanced Linear and Matrix Algebra},
  author={Johnston, N.},
  isbn={9783030528140},
  url={https://books.google.ae/books?id=LIOTzQEACAAJ},
  year={2021},
  publisher={Springer International Publishing}
}

@misc{spektralzerleger,
  author       = {Eugen Dizer},
  howpublished = {https://spektralzerleger.github.io/gauge-fields-solutions/},
}

@misc{fionn,
  author       = {Fionn Fitzmaurice},
  howpublished = {https://github.com/fionn/gfkg/},
}

@misc{conn,
  author       = {Margherita Barile},
  howpublished = {https://mathworld.wolfram.com/Arcwise-Connected.html},
}

@book{armstrong2013basic,
  title={Basic Topology},
  author={Armstrong, M.A.},
  isbn={9781475717938},
  series={Undergraduate Texts in Mathematics},
  url={https://books.google.ae/books?id=NJbuBwAAQBAJ},
  year={2013},
  publisher={Springer New York}
}

@book{artin2013algebra,
  title={Algebra: Pearson New International Edition},
  author={Artin, M.},
  isbn={9781292051741},
  url={https://books.google.ae/books?id=UzSpBwAAQBAJ},
  year={2013},
  publisher={Pearson Education}
}

@misc{3843015,
    TITLE = {A representation of $SU(2)$ is self dual},
    AUTHOR = {Gaston Barboza (https://math.stackexchange.com/users/585596/gaston-barboza)},
    HOWPUBLISHED = {Mathematics Stack Exchange},
    NOTE = {URL:https://math.stackexchange.com/q/3843015 (version: 2020-09-28)},
    EPRINT = {https://math.stackexchange.com/q/3843015},
    URL = {https://math.stackexchange.com/q/3843015}
}

@misc{ragone2023representationtheorygeometricquantum,
      title={Representation Theory for Geometric Quantum Machine Learning}, 
      author={Michael Ragone and Paolo Braccia and Quynh T. Nguyen and Louis Schatzki and Patrick J. Coles and Frederic Sauvage and Martin Larocca and M. Cerezo},
      year={2023},
      eprint={2210.07980},
      archivePrefix={arXiv},
      primaryClass={quant-ph},
      url={https://arxiv.org/abs/2210.07980}, 
}

@misc{bronstein2021geometricdeeplearninggrids,
      title={Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges}, 
      author={Michael M. Bronstein and Joan Bruna and Taco Cohen and Petar Veličković},
      year={2021},
      eprint={2104.13478},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2104.13478}, 
}

@book{zee2016group,
  title={Group Theory in a Nutshell for Physicists},
  author={Zee, A.},
  isbn={9780691162690},
  lccn={2015037408},
  series={In a Nutshell},
  url={https://books.google.ae/books?id=DmuYDwAAQBAJ},
  year={2016},
  publisher={Princeton University Press}
}

@misc{rod,
  author       = {Belongie, Serge},
  howpublished = {https://mathworld.wolfram.com/RodriguesRotationFormula.html},
}

@misc{liejb,
  author       = {Baez, John},
  howpublished = {https://math.ucr.edu/home/baez/lie{\_}groups/},
}

@misc{mitocw,
  author       = {MIT OpenCourseWare},
  howpublished = {https://ocw.mit.edu/},
}

@MISC {2309250,
    TITLE = {Are there vector bundles that are not locally trivial?},
    AUTHOR = {Andrew D. Hwang (https://math.stackexchange.com/users/86418/andrew-d-hwang)},
    HOWPUBLISHED = {Mathematics Stack Exchange},
    NOTE = {URL:https://math.stackexchange.com/q/2309250 (version: 2017-06-04)},
    EPRINT = {https://math.stackexchange.com/q/2309250},
    URL = {https://math.stackexchange.com/q/2309250}
}

@misc{qgjb,
  author       = {Baez, John},
  howpublished = {https://math.ucr.edu/home/baez/qg-spring2002/},
}

@misc{quantum_theory,
  title = {Lectures on Quantum Theory},
  author       = {Frederic P. Schuller},
}

@book{lee2006riemannian,
  title={Riemannian Manifolds: An Introduction to Curvature},
  author={Lee, J.M.},
  isbn={9780387227269},
  lccn={97014537},
  series={Graduate Texts in Mathematics},
  url={https://books.google.ae/books?id=92PgBwAAQBAJ},
  year={2006},
  publisher={Springer New York}
}

@misc{ddg_nv,
  title = {DDG notes},
  author       = {Niraj Venkat},
  howpublished = {https://github.com/nirajvenkat/ddg-nv},
}

@misc{aoc,
  title = {Axiom of choice},
  author       = {Brilliant.org},
  howpublished = {https://brilliant.org/wiki/axiom-of-choice/},
}

@misc{newton,
  title = {Newton's Identities},
  author       = {Brilliant.org},
  howpublished = {https://brilliant.org/wiki/newtons-identities/},
}

@book{nakahara2018geometry,
  title={Geometry, Topology and Physics},
  author={Nakahara, M.},
  isbn={9781420056945},
  url={https://books.google.ae/books?id=p2C1DwAAQBAJ},
  year={2018},
  publisher={CRC Press}
}

@misc{Perko,
  title = {KnotPlot Perko Pair},
  author       = {Rob Scharein},
  howpublished = {https://knotplot.com/perko/},
}

@article{van2006visualization,
  title={Visualization of Seifert surfaces},
  author={Van Wijk, Jarke J and Cohen, Arjeh M},
  journal={IEEE Transactions on Visualization and Computer Graphics},
  volume={12},
  number={4},
  pages={485--496},
  year={2006},
  publisher={IEEE}
}

@misc{t2_notes,
  title = {Topology {\&} Geometry at AIMS},
  author       = {Tadashi Tokieda (NV notes)},
}

@book{adams2004knot,
  title={The Knot Book},
  author={Adams, C.C.},
  year={2004},
  publisher={American Mathematical Society}
}

@misc{julia_seifert,
  title = {Seifert Matrix Computations},
  author       = {Julia Collins},
  howpublished={https://www.maths.ed.ac.uk/~v1ranick/julia/index.htm}
}

@misc{hardy_ac,
  title = {Knot theory notes},
  author       = {Shintaro Fushida-Hardy},
  howpublished={https://stanford.edu/\string~sfh/knot.pdf}
}

@book{simon2023topological,
  title={Topological Quantum},
  author={Simon, S.H.},
  isbn={9780198886778},
  url={https://books.google.ae/books?id=1fjYEAAAQBAJ},
  year={2023},
  publisher={OUP Oxford}
}

@book{lancaster2014quantum,
  title={Quantum Field Theory for the Gifted Amateur},
  author={Lancaster, T. and Blundell, S.},
  isbn={9780199699322},
  lccn={2013950755},
  url={https://books.google.ae/books?id=0rkVDAAAQBAJ},
  year={2014},
  publisher={OUP Oxford}
}

@article{Shoshany2021_OGRe,
    author    = {Barak Shoshany},
    doi       = {10.21105/joss.03416},
    journal   = {Journal of Open Source Software},
    number    = {65},
    pages     = {3416},
    publisher = {The Open Journal},
    title     = {OGRe: An Object-Oriented General Relativity Package for Mathematica},
    url       = {https://doi.org/10.21105/joss.03416},
    volume    = {6},
    year      = {2021}
}

@MISC {1446788,
    TITLE = {Leibniz rule for covariant derivative of tensor fields},
    AUTHOR = {Jack Lee (https://math.stackexchange.com/users/1421/jack-lee)},
    HOWPUBLISHED = {Mathematics Stack Exchange},
    NOTE = {URL:https://math.stackexchange.com/q/1446788 (version: 2015-09-22)},
    EPRINT = {https://math.stackexchange.com/q/1446788},
    URL = {https://math.stackexchange.com/q/1446788}
}

@book{schutz2009first,
  title={A First Course in General Relativity},
  author={Schutz, B.},
  isbn={9780521887052},
  lccn={2009497226},
  url={https://books.google.ae/books?id=V1CGLi58W7wC},
  year={2009},
  publisher={Cambridge University Press}
}

@misc{2d_spacetime,
  author = {S.C. Fletcher et al.},
  howpublished={https://sites.socsci.uci.edu/~jmanchak/wtdbwefs.pdf}
}

@MISC {2528632,
    TITLE = {Prove $\det(1+tA)=1+t\cdot tr(A)+O(t^2)$},
    AUTHOR = {ziggurism (https://math.stackexchange.com/users/16490/ziggurism)},
    HOWPUBLISHED = {Mathematics Stack Exchange},
    NOTE = {URL:https://math.stackexchange.com/q/2528632 (version: 2017-11-20)},
    EPRINT = {https://math.stackexchange.com/q/2528632},
    URL = {https://math.stackexchange.com/q/2528632}
}

@book{carroll2019spacetime,
  title={Spacetime and Geometry},
  author={Carroll, S.M.},
  isbn={9781108488396},
  lccn={2019038160},
  url={https://books.google.ae/books?id=PTGdDwAAQBAJ},
  year={2019},
  publisher={Cambridge University Press}
}

@misc{tong,
  author = {David Tong},
  howpublished={https://www.damtp.cam.ac.uk/user/tong/teaching.html}
}

@book{zee2013einstein,
  title={Einstein Gravity in a Nutshell},
  author={Zee, A.},
  isbn={9781400847457},
  series={In a Nutshell},
  url={https://books.google.com/books?id=5Dy1hlKvmCYC},
  year={2013},
  publisher={Princeton University Press}
}

@book{zee2010quantum,
  title={Quantum Field Theory in a Nutshell: (Second Edition)},
  author={Zee, A.},
  isbn={9780691140346},
  lccn={2009015469},
  series={In a Nutshell},
  url={https://books.google.ae/books?id=XrumDwAAQBAJ},
  year={2010},
  publisher={Princeton University Press}
}

@misc{Bertschinger02,
  author = {Edmund Bertschinger},
  howpublished={https://ncatlab.org/nlab/show/Einstein-Hilbert+action{\#}Bertschinger02}
}