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 = (p)r acts freely on a product of k spheres Sn1 × × Snk, then r k. We prove this conjecture in the case where the dimensions {ni} are high compared to all the differences |ni nj| 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/