Complexity of relations in the braid group
Group Theory
2009-06-02 v1 Geometric Topology
Abstract
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.
Cite
@article{arxiv.0906.0137,
title = {Complexity of relations in the braid group},
author = {Joel Hass and Arkadius Kalka and Tahl Nowik},
journal= {arXiv preprint arXiv:0906.0137},
year = {2009}
}