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Topology/Geometry Seminar
Thursday, December 8, 2005
5:30pm,
260 Hawthorn (Altoona)
Michael Jackson
University of Rochester
On the homotopy rank of rank two finite groups
Abstract: Recall that the rank of a finite group is the largest rank of an elementary abelian subgroup. We define the homotopy rank of a finite group to be the smallest number of spheres such that the group acts freely on a finite complex with the homotopy type of the product of those spheres. Benson and Carlson have conjectured that for a finite group the rank and the homotopy rank are the same. Recall that the group Qd(p) for an odd prime p is the semidirect product of a rank two elementary abelian p-group by SL(2,p). In this talk we will show that any rank two group that does not have a subquotient isomorphic to Qd(p) for any prime p has a homotopy rank of two.
We meet weekly on Thursday afternoons, with the third meeting of each month in Altoona. If you are interested in giving a talk in our seminar please contact one of the coordinators for the Fall 2005 semester: Aissa Wade and Wojciech Dorabiala.
