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Proceedings of the American Mathematical Society

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Isotopic closed nonconjugate braids

Authors: K. Murasugi and R. S. D. Thomas
Journal: Proc. Amer. Math. Soc. 33 (1972), 137-139
MSC: Primary 55A25
MathSciNet review: 0292061
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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)

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Keywords: Braid group, closed braid, conjugate braid, knot, composite knot, oriented knot
Article copyright: © Copyright 1972 American Mathematical Society

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