On the structure of the centralizer of a braid

By Juan González-Meneses, Bert Wiest. 2003

63 citations recorded by the source corpus.

Abstract The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and direct products of mixed braid groups. Then we construct a generating set of the centralizer of any braid on n strands, which has at most k ( k + 1 ) 2 elements if n = 2 k , and at most k ( k + 3 ) 2 elements if n = 2 k + 1 . These bounds are shown to be sharp, due to work of N.V. Ivanov and of S.J. Lee. Finally, we describe how one can explicitly compute this generating set.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2826e860a2ac5a88ab2cc085a787a3db8d22a867

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Basic results on braid groups (2010, methodology): “Algebraically, Z ( α ) is the braid group of an annulus, that is, the fundamental group of the conﬁguration space of several points in an annulus (see [45]).”
Foundations of Garside Theory (2013, background): “The complete description of the normalizers and centralize rs in Paris [187], González-Meneses–Wiest [141], and Godelle [132, 133] heavily re ies on the existence of a Garside element and the properties of the derived normal dec ompositions.”
Conjugacy in Garside groups I: cyclings, powers and rigidity (2006, background): “It is known [25, 24] that if X is pseudo-Anosov, every element in the centralizer of X has a common power with X , up to multiplication by a central power of ∆.”