Free actions on products of spheres at high dimensions

Okutan, Osman Berat; Yalçın, Ergün

doi:10.2140/agt.2013.13.2087

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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

DOI: 10.2140/agt.2013.13.2087

Abstract

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

Keywords

rank conjecture, products of spheres, Tate cohomology

Mathematical Subject Classification 2010

Primary: 57S25

Secondary: 20J06

References

Publication

Received: 17 October 2012

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/

Volume 13, issue 4 (2013)