turkmath.org

I will give a survey of problems and recent results on finite group actions on products of spheres. The general problem in this field is to classify all finite groups which can act freely on a product of k many spheres for a given positive integer k. One of the classical conjectures states that if a finite group acts freely on a product of k spheres, then the rank of the group must be less than or equal to k. We recently proved a special case of this conjecture with Osman Berat Okutan. I will explain some of the ideas behind the proof.