Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Isotopic closed nonconjugate braids


Authors: K. Murasugi and R. S. D. Thomas
Journal: Proc. Amer. Math. Soc. 33 (1972), 137-139
MSC: Primary 55A25
DOI: https://doi.org/10.1090/S0002-9939-1972-0292061-0
MathSciNet review: 0292061
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: J. S. Birman has conjectured that, when a knot is represented by a closed braid on a minimal number n of strands, the conjugacy class of the braid exhausts the set of braids in $ {B_n}$ closing to define the knot. Counterexamples are given to disprove the conjecture, even when it is weakened to refer only to oriented knots.


References [Enhancements On Off] (What's this?)

  • [1] J. S. Birman, Non-conjugate braids can define isotopic knots, Comm. Pure Appl. Math. 22 (1969), 239-242. MR 39 #6298. MR 0244985 (39:6298)
  • [2] R. H. Fox, On the total curvature of some tame knots, Ann. of Math. (2) 52 (1950), 258-260. MR 12, 273. MR 0037510 (12:273d)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55A25

Retrieve articles in all journals with MSC: 55A25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0292061-0
Keywords: Braid group, closed braid, conjugate braid, knot, composite knot, oriented knot
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society