# Honors Oral Exam

## Groups acting freely on products of spheres and the cohomology of groups

Kenneth Plante

Thursday, May 10th, 2018
2:00 PM - 3:00 PM
Hylan 1106A

In this talk, we explore free group actions using the techniques of group cohomology. In particular, we are interested in free actions of finite abelian groups on products of spheres. It is known that the only finite abelian groups which act freely on a single sphere are cyclic. As a generalization, it has been conjectured that if p is a prime and $(Z_p)^r$ acts freely on a product of k spheres, then $% $ This conjecture in its full generality remains open, but partial results are known. We will use the long exact sequence for Tate cohomology to prove the case where the spheres are equidimensional (and the action is trivial on homology), and see how group cohomology arises in the solution to this problem.

Event contact: hazel dot mcknight at rochester dot edu