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 .
"Noncrossing partitions and Milnor fibers." Algebr. Geom. Topol. 18 (7) 3821 - 3838, 2018. https://doi.org/10.2140/agt.2018.18.3821