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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
DOI: https://doi.org/10.1090/S0002-9947-1993-1179401-3
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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Keywords: <IMG WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$3$">-manifold, open book decomposition, link, knot, braid, Markov equivalence
Article copyright: © Copyright 1993 American Mathematical Society