Algebraic & Geometric Topology

The homology of the Milnor fiber for classical braid groups

Filippo Callegaro

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796610

Digital Object Identifier
doi:10.2140/agt.2006.6.1903

Mathematical Reviews number (MathSciNet)
MR2263054

Zentralblatt MATH identifier
1166.20044

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

Keywords
braid groups Milnor fiber local system

Citation

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. https://projecteuclid.org/euclid.agt/1513796610


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