Volume 13, issue 4 (2013)

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Free actions on products of spheres at high dimensions

Osman Berat Okutan and Ergün Yalçın

Algebraic & Geometric Topology 13 (2013) 2087–2099
Abstract

A classical conjecture in transformation group theory states that if $G={\left(ℤ∕p\right)}^{r}$ acts freely on a product of $k$ spheres ${S}^{{n}_{1}}×\cdots ×{S}^{{n}_{k}}$, then $r\le k$. We prove this conjecture in the case where the dimensions $\left\{{n}_{i}\right\}$ are high compared to all the differences $|{n}_{i}-{n}_{j}|$ between the dimensions.

Keywords
rank conjecture, products of spheres, Tate cohomology
Primary: 57S25
Secondary: 20J06