Geometry and Topology Seminar | Ergun Yalcin | Free Actions on Products of Real Projective Spaces

There are many conjectures on restrictions on finite groups that can act freely on a topological space with prescribed homotopy type. The most famous of these conjectures is the rank conjecture, which claims that if an elementary abelian p-group of rank r acts freely on a product of k spheres, then r is less than or equal to k. In 1983, Cusick made a similar conjecture for free actions on products of real projective spaces. We recently solved the homotopy-theoretic version of Cusick’s conjecture. I will explain some of the main ideas used in the proof of this conjecture, after introducing the necessary background.

MC 5417