  The purpose of this note is to complete the study, begun in the first
author's PhD thesis, of the topology of the poset of generalized noncrossing
partitions associated to real reflection groups. In particular, we calculate
the Euler characteristic of this poset with the maximal and minimal elements
deleted. As we show, the result on the Euler characteristic extends to
generalized noncrossing partitions associated to well-generated complex
reflection groups.
