Nonsmoothable involutions on spin 4-manifolds

Abstract

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

8 pages

References in corpus (1)

• Bauer-Furuta invariants under Z_2-actions