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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On the number of closed braids obtained as a result of single stabilizations and destabilizations of a closed braid


Author: A. V. Malyutin
Original publication: Algebra i Analiz, tom 18 (2006), nomer 6.
Journal: St. Petersburg Math. J. 18 (2007), 1011-1020
MSC (2000): Primary 20F36, 57M25
Published electronically: October 2, 2007
MathSciNet review: 2307359
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Abstract | References | Similar Articles | Additional Information

Abstract: Sufficient conditions for a closed $ n$-braid $ \widehat{\beta}$ to have infinite sets $ {\mathfrak{D}}(\widehat{\beta})$ and $ {\mathfrak{S}}(\widehat{\beta})$ are given, where $ {\mathfrak{D}}(\widehat{\beta})$ denotes the set of all closed $ (n-1)$-braids that are obtained from $ \widehat{\beta}$ via Markov destabilization, while $ {\mathfrak{S}}(\widehat{\beta})$ denotes the set of all closed $ (n+1)$-braids that are obtained from $ \widehat{\beta}$ via Markov stabilization. New integer-valued conjugacy invariants for the braid group are introduced.


References [Enhancements On Off] (What's this?)

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Additional Information

A. V. Malyutin
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: malyutin@pdmi.ras.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-07-00980-6
PII: S 1061-0022(07)00980-6
Keywords: Braid group, Markov destabilization, Markov stabilization, conjugacy invariant, link theory
Published electronically: October 2, 2007
Article copyright: © Copyright 2007 American Mathematical Society