Noncrossing partitions and milnor fibers

Thomas Brady, Michael J Falk, Colum Watt

Research output: Contribution to journalArticle

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 ΔW 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 ΔW .

Original languageEnglish (US)
Pages (from-to)3821-3838
Number of pages18
JournalAlgebraic and Geometric Topology
Volume18
Issue number7
DOIs
StatePublished - Dec 11 2018

ASJC Scopus subject areas

  • Geometry and Topology

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