Volume 11, issue 5 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 4, 1827–2458
Issue 3, 1253–1825
Issue 2, 621–1251
Issue 1, 1–620

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Reducible braids and Garside Theory

Juan González-Meneses and Bert Wiest

Algebraic & Geometric Topology 11 (2011) 2971–3010

We show that reducible braids which are, in a Garside-theoretical sense, as simple as possible within their conjugacy class, are also as simple as possible in a geometric sense. More precisely, if a braid belongs to a certain subset of its conjugacy class which we call the stabilized set of sliding circuits, and if it is reducible, then its reducibility is geometrically obvious: it has a round or almost round reducing curve. Moreover, for any given braid, an element of its stabilized set of sliding circuits can be found using the well-known cyclic sliding operation. This leads to a polynomial time algorithm for deciding the Nielsen–Thurston type of any braid, modulo one well-known conjecture on the speed of convergence of the cyclic sliding operation.

braid group, Garside group, Nielsen–Thurston classification, algorithm
Mathematical Subject Classification 2010
Primary: 20F10, 20F36
Received: 10 May 2011
Accepted: 28 June 2011
Published: 25 November 2011
Juan González-Meneses
Departamento de Álgebra
Facultad de Matemáticas
Universidad de Sevilla
Apdo 1160
41080 Sevilla
Bert Wiest
UFR Mathématiques (UMR 6625 du CNRS)
Université de Rennes 1
Campus de Beaulieu
35042 Rennes Cedex