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Cabling Burau Representation

Christian Blanchet·Ivan Marin
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Abstract

The Burau representation enables to define many other representations of the braid group $B_n$ by the topological operation of ``cabling braids''. We show here that these representations split into copies of the Burau representation itself and of a representation of $B_n/(P_n,P_n)$. In particular, we show that there is no gain in terms of faithfulness by cabling the Burau representation.

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Christian Blanchet, Ivan Marin. 2007-01-06. Cabling Burau Representation. https://arxiv.org/abs/math/0701189

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