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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
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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.


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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