Algebraic & Geometric Topology

Noncrossing partitions and Milnor fibers

Thomas Brady, Michael J Falk, and Colum Watt

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Abstract

For a finite real reflection group W we use noncrossing partitions of type W to construct finite cell complexes with the homotopy type of the Milnor fiber of the associated W –discriminant Δ W and that of the Milnor fiber of the defining polynomial of the associated reflection arrangement. These complexes support natural cyclic group actions realizing the geometric monodromy. Using the shellability of the noncrossing partition lattice, this cell complex yields a chain complex of homology groups computing the integral homology of the Milnor fiber of Δ W .

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 7 (2018), 3821-3838.

Dates
Received: 16 June 2017
Revised: 12 June 2018
Accepted: 21 June 2018
First available in Project Euclid: 18 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.agt/1545102055

Digital Object Identifier
doi:10.2140/agt.2018.18.3821

Mathematical Reviews number (MathSciNet)
MR3892232

Zentralblatt MATH identifier
07006378

Subjects
Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 05E99: None of the above, but in this section

Keywords
Milnor fibers finite reflection groups generalized braid groups noncrossing partitions

Citation

Brady, Thomas; Falk, Michael J; Watt, Colum. Noncrossing partitions and Milnor fibers. Algebr. Geom. Topol. 18 (2018), no. 7, 3821--3838. doi:10.2140/agt.2018.18.3821. https://projecteuclid.org/euclid.agt/1545102055


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