Conjugacy in Garside Groups III: Periodic braids
| dc.creator | Birman, Joan S. | |
| dc.creator | Gebhardt, Volker | |
| dc.creator | Gonzalez-Meneses, Juan | |
| dc.date | 2006-09-21 | |
| dc.date | 2007-02-22 | |
| dc.date.accessioned | 2026-07-07T07:47:59Z | |
| dc.date.available | 2026-07-07T07:47:59Z | |
| dc.description | An element in Artin's braid group B_n is said to be periodic if some power of it lies in the center of B_n. In this paper we prove that all previously known algorithms for solving the conjugacy search problem in B_n 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 B_n 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 B_n, 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. | |
| dc.description | 33 pages, 13 figures. Classical references implying Corollaries 12 and 15 have been added. To appear in Journal of Algebra | |
| dc.identifier | https://arxiv.org/abs/math/0609616 | |
| dc.identifier | http://arxiv.org/abs/math/0609616 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124349 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 20F36; 20F10 | |
| dc.title | Conjugacy in Garside Groups III: Periodic braids | |
| dc.type | text |