On the length of cohomology spheres

Abstract

We present the length, a numerical cohomological index theory, of $G$-spaces which are cohomology spheres and $G$ is a $p$-torus or a torus group, where $p$ is a prime. As a consequence, we obtain Borsuk-Ulam and Bourgin-Yang type theorems in this context. A sharper version of the Bourgin-Yang theorem for topological manifolds is also proved. Also, we give some general results regarding the upper and lower bound for the length.