Geodesic
Noncrossing partitions and Milnor fibers
Brady, Thomas1 ; Falk, Michael2 ; Watt, Colum3
1 School of Mathematical Sciences, Dublin City University, Dublin, Ireland
2 Department Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ, United States
3 School of Mathematical Sciences, Dublin Institute of Technology, Dublin, Ireland
Algebraic and Geometric Topology, Tome 18 (2018) no. 7, pp. 3821-3838

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2018.18.3821
Keywords: Milnor fibers, finite reflection groups, generalized braid groups, noncrossing partitions

Brady, Thomas 1 ; Falk, Michael 2 ; Watt, Colum 3

1 School of Mathematical Sciences, Dublin City University, Dublin, Ireland
2 Department Mathematics and Statistics, Northern Arizona University, Flagstaff, AZ, United States
3 School of Mathematical Sciences, Dublin Institute of Technology, Dublin, Ireland 
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Brady, Thomas; Falk, Michael; Watt, Colum. Noncrossing partitions and Milnor fibers. Algebraic and Geometric Topology, Tome 18 (2018) no. 7, pp. 3821-3838. doi: 10.2140/agt.2018.18.3821

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