Algebra and Topology Seminar

4pm Tuesday 16 November 2004
Carlo Casolo
University of Florence

The homotopy type of the p-subgroup complex of a finite group

Given a finite group G and a prime p, the p-subgroup complex (or the Brown complex) S_p(G) of G at p is the chain complex of the partially ordered set of all non-trivial p-subgroups of G. Its relevance has been pointed out by Quillen in a paper of 1978, where he observed in particular that if G is a finite group of Lie type in characteristic p then S_p(G) is strictly related to the building of G (it is in fact homotopy equivalent to it). Since then, interest in the Brown complex (or, rather, in one of its variations called the Quillen complex) has developed along different directions. In the talk I will concentrate on the problem of describing the homotopy type of S_p(G), presenting some new results (in particular for the case of soluble groups), and some open questions.




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