Free Actions on Products of Spheres at High Dimensions

Abstract

A classical conjecture in transformation group theory states that if $G=(\mathbb{Z}/p{)}^r$ acts freely on a product of $k$ spheres $S^{n_1}\times ...\times S^{n_k}$, then $r\le k$. We prove this conjecture in the case where the average of the dimensions $n_i$ is large compared to the differences $|n_i-n_j|$ between the dimensions.

13 pages

References in corpus (1)

• The stable free rank of symmetry of products of spheres