Bibliography
Published online by Cambridge University Press: 27 August 2021
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- The Calculus of Braids , pp. 242 - 243Publisher: Cambridge University PressPrint publication year: 2021
References
Birman, J., Ko, K.H., and Lee, S.J.. 1998. A new approach to the word problem in the braid groups. Adv. Math., 139-2, 322–353.CrossRefGoogle Scholar
Dehornoy, P. 1993. Complexité et décidabilité, Série Mathématiques & Applications, vol. 12, Springer, Paris.Google Scholar
Dehornoy, P. 2004. Braid-based cryptography. In Group Theory, Statistics, and Cryptography, Contemp. Math., vol. 360, Amer. Math. Soc. Providence, RI, pp. 5–33.Google Scholar
Dehornoy, P. 2017. Multifraction reduction I: The 3-Ore case and Artin-Tits groups of type FC. J. Comb. Algebra, 1, 185–228.Google Scholar
Dehornoy, P. 2017. Multifraction reduction II: Conjectures for Artin-Tits groups. J. Comb. Algebra, 1, 229–287.CrossRefGoogle Scholar
Dehornoy, P. 2019. A cancellativity criterion for presented monoids. Semigroup Forum, 99, 368–390.CrossRefGoogle Scholar
Dehornoy, P., Dynnikov, I., Rolfsen, D., and Wiest, B.. 2008. Ordering Braids, Mathematical Surveys and Monographs, vol. 148, Amer. Math. Soc., Providence, RI.Google Scholar
Dynnikov, I. 2002. On a Yang-Baxter mapping and the Dehornoy ordering. Uspekhi Mat. Nauk, 57-3, 151–152. English translation in Russian Math. Surveys, 57-3, 592–594.Google Scholar
Epstein, D., Cannon, J., Holt, D., Levy, S., Paterson, M., and Thurston, W.. 1992. Word Processing in Groups, Jones & Bartlett Publ., Boston.Google Scholar
Fromentin, J. 2011. Every braid admits a short sigma-definite expression. J. Eur. Math. Soc., 13, 1591–1631.Google Scholar
Fromentin, J. and Paris, L.. 2012. A simple algorithm for finding short sigma-definite representatives. J. Algebra, 350, 405–415.Google Scholar
Garside, F.A. 1969. The braid group and other groups. Quart. J. Math. Oxford, 20-78, 235–254.Google Scholar
Gebhardt, V. and González-Meneses, J.. 1969. The cyclic sliding operation in Garside groups. Math. Z., 265, 85–114.CrossRefGoogle Scholar
Guaschi, J. and Juan-Pineda, D.. 2015. A survey of surface braid groups and the lower algebraic K-theory of their group rings. In Handbook of Group Actions, Volume II Adv. Lect. Math., vol. 32, International Press of Boston Inc., Somerville, MA, pp. 23–75.Google Scholar
Kassel, C. and Turaev, V.. 2008. Braid Groups, Grad. Texts in Math., Springer, New York.CrossRefGoogle Scholar
Ko, K.H., Lee, S.J., Cheon, J.H., Han, J.W., Kang, J.S., and C. Park. 2000. New public-key cryptosystem using braid groups. In Advances in Cryptology – CRYPTO 2000, Springer Lect. Notes in Comput. Sci., vol 1880, Springer, Berlin, pp. 166–184.Google Scholar
Laver, R. 1996. Braid group actions on left distributive structures, and well orderings in the braid groups. J. Pure Appl. Algebra, 108, 81–98.Google Scholar
Moody, J.A. 1991. The Burau representation of the braid group Bn is unfaithful for large n. Bull. Amer. Math. Soc., 25, 379–384.Google Scholar
Schleimer, S. 2008. Polynomial-time word problems. Comm. Math. Helv., 83, 741–765.CrossRefGoogle Scholar