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Braid Groups are Linear

Stephen J. Bigelow
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Abstract

The braid groups B_n can be defined as the mapping class group of the n-punctured disc. The Lawrence-Krammer representation of the braid group B_n is the induced action on a certain twisted second homology of the space of unordered pairs of points in the n-punctured disc. Recently, Daan Krammer showed that this is a faithful representation in the case n=4. In this paper, we show that it is faithful for all n.

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Stephen J. Bigelow. 2000-05-04. Braid Groups are Linear. https://arxiv.org/abs/math/0005038

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