Paper published by Geometry and Topology

From: Geometry and Topology Journal (gt_at_maths.warwick.ac.uk)
Date: 09/29/04 

Date: Wed, 29 Sep 2004 13:30:03 +0000 (UTC)

The following paper has been published:

Geometry and Topology, Volume 8 (2004) Paper no. 35, pages 1281--1300

URL:
http://www.maths.warwick.ac.uk/gt/GTVol8/paper35.abs.html

Title:
The proof of Birman's conjecture on singular braid monoids

Author(s):
Luis Paris

Abstract:

Let B_n be the Artin braid group on n strings with standard generators
sigma_1, ..., sigma_{n-1}, and let SB_n be the singular braid monoid
with generators sigma_1^{+-1}, ..., sigma_{n-1}^{+-1}, tau_1, ...,
tau_{n-1}. The desingularization map is the multiplicative
homomorphism eta: SB_n --> Z[B_n] defined by eta(sigma_i^{+-1}) =
_i^{+-1} and eta(tau_i) = sigma_i - sigma_i^{-1}, for 1 <= i <=
n-1. The purpose of the present paper is to prove Birman's conjecture,
namely, that the desingularization map eta is injective.

AMS Classification Numbers. Primary: 20F36
Secondary: 57M25. 57M27

Keywords:
Singular braids, desingularization, Birman's conjecture

Received: 6 January 2004
Revised: 21 September 2004
Accepted: 21 September 2004
Published: 28 September 2004

Proposed: Joan Birman
Seconded: Robion Kirby, Cameron Gordon

Author(s) address(es):
Institut de Mathematiques de Bourgogne, Universite de Bourgogne
UMR 5584 du CNRS, BP 47870, 21078 Dijon cedex, France
Email: lparis@u-bourgogne.fr
URL: http://math.u-bourgogne.fr/topo/paris/index.html