An algorithm for the word problem in braid groups

Details An algorithm for the word problem in braid groups An algorithm for the word problem in braid groups

2002-11-11

arxiv.org/abs/math/0211169v1

Mathematics

Geometric Topology

17 pages, 6 figures

Scientific paper

We suggest a new algorithm for finding a canonical representative of a given braid, and also for the harder problem of finding a $\sigma_1$-consistent representative. We conjecture that the algorithm is quadratic-time. We present numerical evidence for this conjecture, and prove two results: (1) The algorithm terminates in finite time. (2) The conjecture holds in the special case of 3-string braids - in fact, we prove that the algorithm finds a minimal-lenght representative for any 3-string braid.

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