Equivariant CW-complexes and group actions on spheres
Ian Hambleton (McMaster University)
Monday 19th January, 2009 16:00-17:00 Mathematics Building, room 214
(joint work with Semra Pamuk and Ergun Yalcin). In the talk I will describe an approach to an open problem: which finite groups of rank 2 can act on spheres with rank 1 isotropy ? The idea is to construct periodic projective resolutions over the orbit category, based on work of tom Dieck and Lueck, and then to prove a realization theorem to obtain a geometric action with prescribed isotropy. As an application, we show that the symmetric group $G=S_5$ admits a finite $G$-CW complex $X$ homotopy equivalent to a sphere, with cyclic isotropy subgroups.