On the centralizer of generic braids

Author:

González-Meneses Juan1,Valladares Dolores1

Affiliation:

1. Departamento de Álgebra , Instituto de Matemáticas (IMUS) , Universidad de Sevilla , Av. Reina Mercedes s/n, 41012 Sevilla , Spain

Abstract

Abstract We study the centralizer of a braid from the point of view of Garside theory, showing that generically a minimal set of generators can be computed very efficiently, as the ultra summit set of a generic braid has a very particular structure. We present an algorithm to compute the centralizer of a braid whose generic-case complexity is quadratic on the length of the input, and which outputs a minimal set of generators in the generic case.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference26 articles.

1. E. Artin, Theorie der Zöpfe, Abh. Math. Semin. Univ. Hambg. 4 (1925), no. 1, 47–72.

2. E. Artin, Theory of braids, Ann. of Math. (2) 48 (1947), 101–126.

3. J. Birman, K. H. Ko and S. J. Lee, A new approach to the word and conjugacy problems in the braid groups, Adv. Math. 139 (1998), no. 2, 322–353.

4. J. S. Birman, V. Gebhardt and J. González-Meneses, Conjugacy in Garside groups. I. Cyclings, powers and rigidity, Groups Geom. Dyn. 1 (2007), no. 3, 221–279.

5. J. S. Birman, V. Gebhardt and J. González-Meneses, Conjugacy in Garside groups. II. Structure of the ultra summit set, Groups Geom. Dyn. 2 (2008), no. 1, 13–61.

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