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2018 Noncrossing partitions and Milnor fibers
Thomas Brady, Michael J Falk, Colum Watt
Algebr. Geom. Topol. 18(7): 3821-3838 (2018). DOI: 10.2140/agt.2018.18.3821

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 .

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Thomas Brady. Michael J Falk. Colum Watt. "Noncrossing partitions and Milnor fibers." Algebr. Geom. Topol. 18 (7) 3821 - 3838, 2018. https://doi.org/10.2140/agt.2018.18.3821

Information

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

zbMATH: 07006378
MathSciNet: MR3892232
Digital Object Identifier: 10.2140/agt.2018.18.3821

Subjects:
Primary: 20F55
Secondary: 05E99, 52C35

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 7 • 2018
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