Document Type
Article
Rights
Available under a Creative Commons Attribution Non-Commercial Share Alike 4.0 International Licence
Disciplines
Pure mathematics
Abstract
For a finite real reflection group, W, we use non-crossing partitions of type W to construct a finite cell complex with the homotopy type of the Milnor fiber of the associated W–discriminant, Δ_W, and another with the homotopy type 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 non-crossing partition lattice, this cell complex yields a chain complex of homology groups computing the integral homology of the Milnor fiber of Δ_W.
DOI
https://doi.org/10.2140/agt.2018.18.3821
Recommended Citation
Brady, T., Falk, M. J., & Watt, C. (2018). Noncrossing partitions and milnor fibers. Algebraic and Geometric Topology, 18(7), 3821-3838. DOI: 10.2140/agt.2018.18.3821
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Details
Algebraic and Geometric Topology, Volume 18, No. 7, pp 3821-3838, (2018)