Conjugacy in Garside groups III : periodic braids

Joan S. Birman, Volker Gebhardt, Juan González-Meneses

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

Abstract

An element in Artin's braid group Bn is said to be periodic if some power of it lies in the center of Bn. In this paper we prove that all previously known algorithms for solving the conjugacy search problem in Bn are exponential in the braid index n for the special case of periodic braids. We overcome this difficulty by putting to work several known isomorphisms between Garside structures in the braid group Bn and other Garside groups. This allows us to obtain a polynomial solution to the original problem in the spirit of the previously known algorithms. This paper is the third in a series of papers by the same authors about the conjugacy problem in Garside groups. They have a unified goal: the development of a polynomial algorithm for the conjugacy decision and search problems in Bn, which generalizes to other Garside groups whenever possible. It is our hope that the methods introduced here will allow the generalization of the results in this paper to all Artin-Tits groups of spherical type.
Original languageEnglish
Pages (from-to)746-776
Number of pages31
JournalJournal of Algebra
Volume316
Issue number2
Publication statusPublished - 15 Oct 2007

Keywords

  • group theory
  • mathematics

Fingerprint

Dive into the research topics of 'Conjugacy in Garside groups III : periodic braids'. Together they form a unique fingerprint.

Cite this