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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 S4 and S2 ×S2 admits a homologically trivial, pseudofree, locally linear action of Zp 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

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