#### Volume 11, issue 3 (2011)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
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 ${S}^{4}$ and ${S}^{2}×{S}^{2}$ 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
Primary: 57M60
Secondary: 57R57
##### 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