Topology of eigenspace posets for unitary reflection groups

The eigenspace theory of unitary reflection groups, initiated by Springer and Lehrer, suggests that the following object is worthy of study: the poset of eigenspaces of elements of a unitary reflection group, for a fixed eigenvalue, ordered by the reverse of inclusion. We investigate topological properties of this poset. The new results extend the well-known work of Orlik and Solomon on the lattice of intersections of hyperplanes.