Ian Hambleton

In the talk I will survey some results, techniques, and open problems, concerning finite group actions on (i) spheres, (ii) products of spheres and (iii) non-compact space forms modelled on indefinite quadratic forms.

The unit spheres in orthogonal representations of finite groups give examples of group actions on spheres. We investigate non-linear actions by studying chain complexes over the orbit category, and constructing finite G-CW complexes. This leads to...

I will discuss finite group actions on integral or rational homology 3-spheres. The main examples for this talk are the Brieskorn integral homology 3-spheres M(p,q,r) arising from isolated singularities, which bound smooth 4-manifolds with definite...