turkmath.org

Actions of finite groups on spheres can be studied in various different geometrical settings, such as (A) smooth G-actions on a closed manifold homotopy equivalent to a sphere, (B) finite G-homotopy representations (as defined by tom Dieck), and (C) finite G-CW complexes homotopy equivalent to a sphere. These three settings generalize the basic models arising from unit spheres S(V) in orthogonal or unitary G-representations. In the talk, I will discuss the group theoretic constraints imposed by assuming that the actions have rank 1 isotropy (meaning that the isotropy subgroups of G do not contain Z/p x Z/p, for any prime p). This is joint work with Ian Hambleton.