The homology of the Milnor fiber for classical braid groups

Callegaro, Filippo

doi:10.2140/agt.2006.6.1903

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The homology of the Milnor fiber for classical braid groups

Filippo Callegaro

Algebraic & Geometric Topology 6 (2006) 1903–1923

DOI: 10.2140/agt.2006.6.1903

arXiv: math.AT/0511453

Abstract

In this paper we compute the homology of the braid groups, with coefficients in the module $ℤ [q^{\pm 1}]$ 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.

Keywords

braid groups, Milnor fiber, local system

Mathematical Subject Classification 2000

Primary: 20F36

Secondary: 20J06, 32S55

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Publication

Received: 30 November 2005

Revised: 22 September 2006

Accepted: 23 September 2006

Published: 14 November 2006

Authors

Filippo Callegaro
Scuola Normale Superiore Piazza dei Cavalieri, 7 56126 Pisa Italy

Volume 6, issue 4 (2006)