Garside-theoretic analysis of Burau representations

2014/01/12 by Calvez, Matthieu, Ito, Tetsuya
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1401.2677

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 simply-nested braids.

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