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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Dehornoy's ordering on the braid group and braid moves

Authors: A. V. Malyutin and N. Yu. Netsvetaev
Translated by: the authors
Original publication: Algebra i Analiz, tom 15 (2003), nomer 3.
Journal: St. Petersburg Math. J. 15 (2004), 437-448
MSC (2000): Primary 57M25
Published electronically: March 30, 2004
MathSciNet review: 2052167
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Abstract: In terms of Dehornoy's ordering on the braid group ${\mathcal B}_n$, restrictions are found that prevent us from performing the Markov destabilization and the Birman-Menasco braid moves. As a consequence, a sufficient condition is obtained for the link represented by a braid to be prime, and it is shown that all braids in ${\mathcal B}_n$ that are not minimal lie in a finite interval of Dehornoy's ordering.

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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

N. Yu. Netsvetaev
Affiliation: St. Petersburg State University, Faculty of Mathematics and Mechanics, Universitetskiĭ pr. 28, Petrodvorets, St. Petersburg 198504, Russia

Received by editor(s): November 23, 2002
Published electronically: March 30, 2004
Additional Notes: Partially supported by the RFBR (grant no. 01-01-01014) and the Russian Ministry of Education (grant PD02-1.1-423).
Article copyright: © Copyright 2004 American Mathematical Society