Homology of the braid group with coefficients in the reduced Burau representation

2014/09/25 by Weiyan Chen, Chen, Weiyan
Mathematics · #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1409.7422

Abstract

The reduced Burau representation V_n of the braid group B_n is obtained from the action of B_n on the homology of an infinite cyclic cover of the n-punctured disc. In this note, we calculate H_*(B_n;V_n) as a module over the Laurent polynomial ring ℚ[t,t^-1].

Related

• Representations of braid groups
• Burau maps and twisted Alexander polynomials
• Cabling Burau Representation
• Linear-central filtrations and the image of the Burau representation
• Gassner and Burau representations over ℤ_p-modules