Volume 11, issue 3 (2011)

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Nonsmoothable group actions on spin $4$–manifolds

Kazuhiko Kiyono

Algebraic & Geometric Topology 11 (2011) 1345–1359
Abstract

We show that every closed, simply connected, spin topological 4–manifold except S4 and S2 × S2 admits a homologically trivial, pseudofree, locally linear action of p for any sufficiently large prime number p which is nonsmoothable for any possible smooth structure.

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Keywords
nonsmoothable group action, spin $4$–manifold, $G$–index of Dirac operator, $10/8$–theorem
Mathematical Subject Classification 2000
Primary: 57M60
Secondary: 57R57
References
Publication
Received: 26 April 2010
Revised: 22 February 2011
Accepted: 16 March 2011
Published: 14 May 2011
Authors
Kazuhiko Kiyono
Graduate School of Mathematical Sciences
The University of Tokyo
3-8-1 Komaba Meguro-ku
Tokyo 153-8914
Japan