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arXiv · 1401.2677

Garside-theoretic analysis of Burau representations

Matthieu Calvez·Tetsuya Ito
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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}.

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Matthieu Calvez, Tetsuya Ito. 2014-01-12. Garside-theoretic analysis of Burau representations. https://arxiv.org/abs/1401.2677

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