Complete simultaneous conjugacy invariants in Garside groups.

Arkadius G. Kalka; Boaz Tsaban; Gary Vinokur

doi:10.48550/arXiv.1403.4622

Complete simultaneous conjugacy invariants in Garside groups.

Arkadius G. Kalka, Boaz Tsaban, Gary Vinokur

Department of Mathematics

Research output: Other contribution

Abstract

We solve the simultaneous conjugacy problem in Artin's braid groups and, more generally, in Garside groups, by means of a complete, effectively computable, finite invariant. This invariant generalizes the one-dimensional notion of super summit set to arbitrary dimensions. One key ingredient in our solution is the introduction of a provable high-dimensional version of the Birman--Ko--Lee cycling theorem. The complexity of this solution is a small degree polynomial in the cardinalities of our generalized super summit sets and the input parameters. Computer experiments suggest that the cardinality of this invariant, for a list of order

Original language	English
Publisher	Cornell University Library, arXiv.org
Volume	abs/1403.4622
DOIs	https://doi.org/10.48550/arXiv.1403.4622
State	Published - 2014

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DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

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Complete simultaneous conjugacy invariants in Garside groups.

Abstract

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