Garside-theoretic analysis of Burau representations
Group Theory
2014-01-17 v2
Abstract
We establish relations between both the classical and the dual Garside structures of the braid group and the Burau representation. Using the classical structure, we formulate a non-vanishing criterion for the Burau representation of the 4-strand braid group. In the dual context, it is shown that the Burau representation for arbitrary braid index is injective when restricted to the set of \emph{simply-nested braids}.
Keywords
Cite
@article{arxiv.1401.2677,
title = {Garside-theoretic analysis of Burau representations},
author = {Matthieu Calvez and Tetsuya Ito},
journal= {arXiv preprint arXiv:1401.2677},
year = {2014}
}