Volume 8, issue 3 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The proof of Birman's conjecture on singular braid monoids

Luis Paris

Geometry & Topology 8 (2004) 1281–1300

arXiv: math.GR/0306422

Abstract

Let Bn be the Artin braid group on n strings with standard generators σ1,,σn1, and let SBn be the singular braid monoid with generators σ1±1,,σn1±1,τ1,,τn1. The desingularization map is the multiplicative homomorphism η: SBn [Bn] defined by η(σi±1) = σi±1 and η(τi) = σi σi1, for 1 i n 1. The purpose of the present paper is to prove Birman’s conjecture, namely, that the desingularization map η is injective.

Keywords
singular braids, desingularization, Birman's conjecture
Mathematical Subject Classification 2000
Primary: 20F36
Secondary: 57M25. 57M27
References
Forward citations
Publication
Received: 6 January 2004
Revised: 21 September 2004
Accepted: 21 September 2004
Published: 28 September 2004
Proposed: Joan Birman
Seconded: Robion Kirby, Cameron Gordon
Authors
Luis Paris
Institut de Mathématiques de Bourgogne
Université de Bourgogne
UMR 5584 du CNRS
BP 47870
21078 Dijon cedex
France