Isotopic closed nonconjugate braids
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- by K. Murasugi and R. S. D. Thomas PDF
- Proc. Amer. Math. Soc. 33 (1972), 137-139 Request permission
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
- Joan S. Birman, Non-conjugate braids can define isotopic knots, Comm. Pure Appl. Math. 22 (1969), 239–242. MR 244985, DOI 10.1002/cpa.3160220207
- R. H. Fox, On the total curvature of some tame knots, Ann. of Math. (2) 52 (1950), 258–260. MR 37510, DOI 10.2307/1969468
Additional Information
- © Copyright 1972 American Mathematical Society
- 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