Cabling Burau Representation

Christian Blanchet (1) , Ivan Marin (2)

1 LMAM - Laboratoire de Mathématiques et Applications des Mathématiques, EA 3885
2 IMJ - Institut de Mathématiques de Jussieu

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.

Domaines: Théorie des représentations [math.RT]; Théorie des groupes [math.GR]

Christian Blanchet, Ivan Marin. Cabling Burau Representation. 2007. ⟨hal-00123496⟩