Nonsmoothable Involutions on Spin 4-Manifolds

Proceedings Mathematical Sciences

Changtao Xue¹  Ximin Liu² 

[1] School of Mathematical Sciences, Dalian University of Technology, Dalian 0, China$$;Department of Mathematics, South China University of Technology, Guangzhou 0, China$$

关键词: Group action;    locally linear;    involution;    nonsmoothable.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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

【 授权许可】

Unknown