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 ${S}^{4}$ 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