Algebraic & Geometric Topology

The homology of the Milnor fiber for classical braid groups

Filippo Callegaro

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In this paper we compute the homology of the braid groups, with coefficients in the module [q±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.

Article information

Algebr. Geom. Topol., Volume 6, Number 4 (2006), 1903-1923.

Received: 30 November 2005
Revised: 22 September 2006
Accepted: 23 September 2006
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F36: Braid groups; Artin groups
Secondary: 20J06: Cohomology of groups 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45]

braid groups Milnor fiber local system


Callegaro, Filippo. The homology of the Milnor fiber for classical braid groups. Algebr. Geom. Topol. 6 (2006), no. 4, 1903--1923. doi:10.2140/agt.2006.6.1903.

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