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Complete simultaneous conjugacy invarian...
Kalka, Arkadius...

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Complete simultaneous conjugacy invariants in Artin's braid groups by Kalka, Arkadius ( Author )
Lemonjar Open Access
Australian National University
01-09-2023
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 $N$ independent elements of Artin's braid group $B_N$, is generically close to~1.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1403.4622
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