Geometry & Topology

The proof of Birman's conjecture on singular braid monoids

Luis Paris

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

singular braids desingularization Birman's conjecture


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.

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