The homology of the Milnor fiber for classical braid groups

Abstract

In this paper we compute the homology of the braid groups, with coefficients in the module $\mathbb{Z}\left[q^{\pm 1}\right]$ given by the ring of Laurent polynomials with integer coefficients and where the action of the braid group is defined by mapping each generator of the standard presentation to multiplication by $-q$.

The homology thus computed is isomorphic to the homology with constant coefficients of the Milnor fiber of the discriminantal singularity.