Dehornoy’s ordering on the braid group and braid moves
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A. V. Malyutin and N. Yu. Netsvetaev
Translated by: the authors - St. Petersburg Math. J. 15 (2004), 437-448
- DOI: https://doi.org/10.1090/S1061-0022-04-00816-7
- Published electronically: March 30, 2004
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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.References
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Bibliographic 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
- N. Yu. Netsvetaev
- Affiliation: St. Petersburg State University, Faculty of Mathematics and Mechanics, Universitetskiĭ pr. 28, Petrodvorets, St. Petersburg 198504, Russia
- Email: nn@pdmi.ras.ru
- 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).
- © Copyright 2004 American Mathematical Society
- Journal: St. Petersburg Math. J. 15 (2004), 437-448
- MSC (2000): Primary 57M25
- DOI: https://doi.org/10.1090/S1061-0022-04-00816-7
- MathSciNet review: 2052167