#### 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
##### Publication
Revised: 13 February 2013
Accepted: 2 March 2013
Published: 31 May 2013
##### Authors
 Osman Berat Okutan Department of Mathematics The Ohio State University Columbus, OH 43210-1174 USA http://www.math.osu.edu/people/okutan.1 Ergün Yalçın Department of Mathematics Bilkent University 06800 Ankara Turkey http://www.fen.bilkent.edu.tr/~yalcine/