Nonsmoothable group actions on spin 4–manifolds

Kiyono, Kazuhiko

doi:10.2140/agt.2011.11.1345

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Nonsmoothable group actions on spin $4$–manifolds

Kazuhiko Kiyono

Algebraic & Geometric Topology 11 (2011) 1345–1359

DOI: 10.2140/agt.2011.11.1345

Abstract

We show that every closed, simply connected, spin topological $4$ –manifold except $S^{4}$ and $S^{2} \times S^{2}$ admits a homologically trivial, pseudofree, locally linear action of $ℤ_{p}$ for any sufficiently large prime number $p$ which is nonsmoothable for any possible smooth structure.

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

Volume 11, issue 3 (2011)