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

Bar-Ilan University

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
Volume	abs/1403.4622
DOIs	https://doi.org/10.48550/arXiv.1403.4622
State	Published - 2014

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https://dblp.org/rec/journals/corr/KalkaTV14

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title = "Complete simultaneous conjugacy invariants in Garside groups.",

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Complete simultaneous conjugacy invariants in Garside groups.

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