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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

The Alexander and Markov theorems via diagrams for links in $ 3$-manifolds


Author: Paul A. Sundheim
Journal: Trans. Amer. Math. Soc. 337 (1993), 591-607
MSC: Primary 57M25; Secondary 57M50
MathSciNet review: 1179401
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Abstract: Let $ M$ be a $ 3$-manifold with an open book decomposition. We obtain a new proof that a link in $ M$ has a braided form and that two braided forms are related by a sequence of two Markov moves for $ M$ by generalizing Morton's approach for links in $ {S^3}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1179401-3
PII: S 0002-9947(1993)1179401-3
Keywords: $ 3$-manifold, open book decomposition, link, knot, braid, Markov equivalence
Article copyright: © Copyright 1993 American Mathematical Society