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Noncrossing partitions and Milnor fibers. (English) Zbl 07006378
Summary: 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 \(\Delta_W\) 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 \(\Delta_W\).
MSC:
20F55 Reflection and Coxeter groups (group-theoretic aspects)
52C35 Arrangements of points, flats, hyperplanes (aspects of discrete geometry)
05E99 Algebraic combinatorics
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