Cabling Burau Representation

Details Cabling Burau Representation Cabling Burau Representation

2007-01-06

arxiv.org/abs/math/0701189v1

Mathematics

Representation Theory

11 pages

Scientific paper

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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