Nonsmoothable involutions on spin 4-manifolds

Changtao Xue; Ximin Liu

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arXiv · 1011.0116

Nonsmoothable involutions on spin 4-manifolds

Changtao Xue·Ximin Liu

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Abstract

Let $X$ be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to $n(-E_8)\bigoplus mH$, where $H$ is the hyperbolic form. In this paper, we prove that for $n$ such that $n\equiv 2 ~{\rm mod} ~4$, there exists a locally linear pseudofree $\mathbb{Z}_2$-action on $X$ which is nonsmoothable with respect to any possible smooth structure on $X$.

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BibTeX RIS

Changtao Xue, Ximin Liu. 2010-10-31. Nonsmoothable involutions on spin 4-manifolds. https://arxiv.org/abs/1011.0116

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