arXiv:0906.0137 Abstract | arXiv Analytics

arXiv:0906.0137 [math.GR]Abstract References Reviews Resources

Complexity of relations in the braid group

Published 2009-05-31Version 1

We show that for any given n, there exists a sequence of words a_k in the generators sigma_1, ... sigma_{n-1} of the braid group B_n, representing the identity element of B_n, such that the number of braid relations of the form sigma_i sigma_{i+1} sigma_i = sigma_{i+1} sigma_i sigma_{i+1} needed to pass from a_k to the empty word is quadratic with respect to the length of a_k.

Categories: math.GR, math.GT

Subjects: 20F36

Keywords: braid group, complexity, identity element, braid relations

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