Geometry & Topology

The proof of Birman's conjecture on singular braid monoids

Luis Paris

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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)=σiσi1, for 1in1. The purpose of the present paper is to prove Birman’s conjecture, namely, that the desingularization map η is injective.

Article information

Source
Geom. Topol., Volume 8, Number 3 (2004), 1281-1300.

Dates
Received: 6 January 2004
Revised: 21 September 2004
Accepted: 21 September 2004
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513883468

Digital Object Identifier
doi:10.2140/gt.2004.8.1281

Mathematical Reviews number (MathSciNet)
MR2087084

Zentralblatt MATH identifier
1057.20029

Subjects
Primary: 20F36: Braid groups; Artin groups
Secondary: 57M25. 57M27

Keywords
singular braids desingularization Birman's conjecture

Citation

Paris, Luis. The proof of Birman's conjecture on singular braid monoids. Geom. Topol. 8 (2004), no. 3, 1281--1300. doi:10.2140/gt.2004.8.1281. https://projecteuclid.org/euclid.gt/1513883468


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