Complete simultaneous conjugacy invariants in Artin's braid groups
نویسندگان
چکیده
We provide the first effectively computable, modulo a mild conjecture, complete invariant for simultaneous conjugacy in Garside groups. This invariant generalizes the notion of super summit set of a conjugacy class, and provides a solution of the simultaneous conjugacy problem in Garside groups, of complexity a small degree polynomial in the sizes of the invariant and the input parameters. Computer experiments suggest that the size of this invariant, for a list of O(N) generic, independent elements of Artin’s braid group BN , is close to 1.
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