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19.81 (2018)

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(Well-known problem). Is the conjugacy problem in the braid group $B_n$ in the class NP (that is, decidable in nondeterministic polynomial time with respect to the maximum of the lengths $|u|, |v|$, where $u, v$ are the input braid words)? A stronger question: given two conjugate elements of $B_n$ represented by braid words of lengths $\leqslant m$, is there a conjugator whose length is bounded by a polynomial function of $m$?

Contributor: V. Shpilrain

Progress

Yes, there is such a conjugator, even for any mapping class groups (J. Tao, Geom. Funct. Anal., 23, no. 1 (2013), 415–466).

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