references.bib

@book{kassel2008braid,
  title={Braid Groups},
  author={Kassel, C. and Dodane, O. and Turaev, V.},
  isbn={9780387685489},
  lccn={2008922934},
  series={Graduate Texts in Mathematics},
  url={https://books.google.co.in/books?id=y6Cox3XjdroC},
  year={2008},
  publisher={Springer New York}
}

@book{lickorish1997,
  title={An Introduction to Knot Theory},
  author={Lickorish, WB Raymond},
  isbn={978-0-387-98254-0},
  series={Graduate Texts in Mathematics},
  year={1997},
  edition={1},
  publisher={Springer New York, NY}
  doi = {https://doi.org/10.1007/978-1-4612-0691-0}
}

@article{10.1215/S0012-7094-00-10131-7, 
author = {Mikhail Khovanov},
title = {{A categorification of the Jones polynomial}},
volume = {101},
journal = {Duke Mathematical Journal},
number = {3},
publisher = {Duke University Press},
pages = {359 -- 426},
abstract = {},
year = {2000},
doi = {10.1215/S0012-7094-00-10131-7},
URL = {https://doi.org/10.1215/S0012-7094-00-10131-7}
}

@article{OlegViro2004,
abstract = {Mikhail Khovanov defined, for a diagram of an oriented classical link, a collection of groups labelled by pairs of integers. These groups were constructed as the homology groups of certain chain complexes. The Euler characteristics of these complexes are the coefficients of the Jones polynomial of the link. The original construction is overloaded with algebraic details. Most of the specialists use adaptations of it stripped off the details. The goal of this paper is to overview these adaptations and show how to switch between them. We also discuss a version of Khovanov homology for framed links and suggest a new grading for it.},
author = {Oleg Viro},
journal = {Fundamenta Mathematicae},
keywords = {Khovanov homology; links; Reidemeister moves},
language = {eng},
number = {1},
pages = {317-342},
title = {Khovanov homology, its definitions and ramifications},
url = {http://eudml.org/doc/282696},
volume = {184},
year = {2004},
}

@article{10.2140/agt.2002.2.337,
author = {Dror Bar-Natan},
title = {On Khovanov's categorification of the Jones polynomial},
volume = {2},
journal = {Algebraic \& Geometric Topology},
number = {1},
publisher = {MSP},
pages = {337 -- 370},
keywords = {categorification, Jones polynomial, Kauffman bracket, Khovanov, knot invariants},
year = {2002},
doi = {10.2140/agt.2002.2.337},
URL = {https://doi.org/10.2140/agt.2002.2.337}
}

@incollection{birman2005braids,
  title={Braids: a survey},
  author={Birman, Joan S and Brendle, Tara E},
  booktitle={Handbook of knot theory},
  pages={19--103},
  year={2005},
  publisher={Elsevier}
}

@article{fassler2005braids,
  title={Braids, the Artin Group, and the Jones Polynomial},
  author={Fassler, Jordan},
  journal={University of California. URl: http://www. math. ucla. edu/\~{} radko/191.1. 05w/jordan. pdf},
  year={2005},
  publisher={Citeseer}
}

@inproceedings{kauffman2016introduction,
  title={An introduction to Khovanov homology},
  author={Kauffman, Louis H},
  booktitle={Knot theory and its applications},
  pages={105--139},
  year={2016}
}

@article{bar2005khovanov,
  title={Khovanov’s homology for tangles and cobordisms},
  author={Bar-Natan, Dror},
  journal={Geometry \& Topology},
  volume={9},
  number={3},
  pages={1443--1499},
  year={2005},
  publisher={Mathematical Sciences Publishers}
}

@article{viro2002remarks,
  title={Remarks on definition of Khovanov homology},
  author={Viro, Oleg},
  journal={arXiv preprint math/0202199},
  year={2002}
}

@book{adams1994knot,
  title={The knot book},
  author={Adams, Colin C},
  year={1994},
  publisher={American Mathematical Soc.}
}

@article{roberts1999knots,
  title={Knots Knotes},
  author={Roberts, Justin},
  journal={Lectures from Edinburgh Course Maths},
  volume={415},
  year={1999}
}

@article{menasco1991tait,
  title={The Tait flyping conjecture},
  author={Menasco, William W and Thistlethwaite, Morwen B},
  year={1991}
}

@article{stoimenow2008tait,
  title={Tait’s conjectures and odd crossing number amphicheiral knots},
  author={Stoimenow, Alexander},
  journal={Bulletin of the American Mathematical Society},
  volume={45},
  number={2},
  pages={285--291},
  year={2008}
}

@article{kauffman2023jones,
  title={The Jones polynomial, Knots, diagrams, and categories},
  author={Kauffman, Louis H},
  journal={Bulletin of the American Mathematical Society},
  volume={60},
  number={4},
  pages={507--537},
  year={2023}
}

@article{kronheimer2011khovanov,
  title={Khovanov homology is an unknot-detector},
  author={Kronheimer, Peter B and Mrowka, Tomasz S},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  volume={113},
  pages={97--208},
  year={2011}
}

@article{traczyk1998new,
  title={A new proof of Markov's braid theorem},
  author={Traczyk, Pawe{\l}},
  journal={Banach Center Publications},
  volume={42},
  number={1},
  pages={409--419},
  year={1998},
  publisher={Polska Akademia Nauk. Instytut Matematyczny PAN}
}

@article{bigelow1999burau,
  title={The Burau representation is not faithful for $n=5$},
  author={Bigelow, Stephen},
  journal={Geometry \& Topology},
  volume={3},
  number={1},
  pages={397--404},
  year={1999},
  publisher={Mathematical Sciences Publishers}
}

@article{long1993burau,
  title={The Burau representation is not faithful for $n\geq 6$},
  author={Long, Darren D and Paton, Michael},
  journal={Topology},
  volume={32},
  number={2},
  pages={439--447},
  year={1993},
  publisher={Pergamon}
}

@article{turner2017five,
  title={Five lectures on Khovanov homology},
  author={Turner, Paul},
  journal={Journal of Knot Theory and Its Ramifications},
  volume={26},
  number={03},
  pages={1741009},
  year={2017},
  publisher={World Scientific}
}

@article{jacobsson2004invariant,
  title={An invariant of link cobordisms from Khovanov homology},
  author={Jacobsson, Magnus},
  journal={Algebraic \& Geometric Topology},
  volume={4},
  number={2},
  pages={1211--1251},
  year={2004},
  publisher={Mathematical Sciences Publishers}
}