Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 18, Number 7 (2018), 3821-3838.
Noncrossing partitions and Milnor fibers
For a finite real reflection group we use noncrossing partitions of type to construct finite cell complexes with the homotopy type of the Milnor fiber of the associated –discriminant 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 .
Algebr. Geom. Topol., Volume 18, Number 7 (2018), 3821-3838.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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