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Noncrossing partitions
and Milnor fibers
Thomas Brady, Michael J Falk and Colum Watt |
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Algebraic & Geometric Topology 18 (2018) 3821–3838
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Abstract |
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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 . |
Keywords
Milnor fibers, finite reflection groups, generalized braid
groups, noncrossing partitions
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Mathematical Subject Classification 2000
Primary: 20F55
Secondary: 52C35, 05E99
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References |
Publication
Received: 16 June 2017
Revised: 12 June 2018
Accepted: 21 June 2018
Published: 11 December 2018
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Authors |
| Thomas Brady | |
| School of Mathematical
Sciences Dublin City University Dublin Ireland |
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| Michael J Falk | |
| Department Mathematics and
Statistics Northern Arizona University Flagstaff, AZ United States |
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| Colum Watt | |
| School of Mathematical
Sciences Dublin Institute of Technology Dublin Ireland |
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