충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제23권3호
  • /
  • Pages.555-561
  • /
  • 2010
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

A POSITIVE PRESENTATION FOR THE PURE BRAID GROUP

  • 투고 : 2010.07.20
  • 심사 : 2010.08.12
  • 발행 : 2010.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

For the pure braid groups, this paper gives a positive finite presentation whose generators are the standard Artin generators, and determines whether the submonoid generated by the Artin generators is a Garside monoid or not.

키워드

참고문헌

  1. E. Artin, Theorie der Zopfe, Abh. Math. Sem. Hamburg 4 (1925), 47-72. https://doi.org/10.1007/BF02950718
  2. J. S. Birman and T.E. Brendle, Braids: A Survey, Handbook of Knot Theory, Elsevier, 2005.
  3. J. S. Birman, V. Gebhardt and J. Gonzalez-Meneses, Conjugacy in Garside groups I: cyclings, powers and rigidity, Groups, Geom. Dyn. 1 (2007), 221-279.
  4. J. S. Birman, K.H. Ko and S.J. Lee, A new approach to the word and conjugacy problems in the braid groups, Adv. Math. 139 (1998), 322-353. https://doi.org/10.1006/aima.1998.1761
  5. P. Dehornoy, Braid groups and left distributive operations, Trans. Amer. Math. Soc. 345 (1994), 115-151. https://doi.org/10.2307/2154598
  6. P. Dehornoy, A fast method for comparing braids, Adv. Math. 125 (1997), 200-235. https://doi.org/10.1006/aima.1997.1605
  7. P. Dehornoy, Groupes de Garside, Ann. Sci. Ecole. Norm. Sup. 35 (2002), 267-306. https://doi.org/10.1016/S0012-9593(02)01090-X
  8. P. Dehornoy and L. Paris, Gaussian groups and Garside groups, two generali- sations of Artin groups, Proc. London Math. Soc. 79 (1999), 569-604. https://doi.org/10.1112/S0024611599012071
  9. F.A. Garside, The braid group and other groups, Quart. J. Math. 20 (1969), 235-254. https://doi.org/10.1093/qmath/20.1.235
  10. D. Margalit and J. McCammond, Geoemtric presentations for the pure braid group, J. Knot Theory Ramif. 18 (2009), 1-20. https://doi.org/10.1142/S0218216509006859