Nonsmoothable involutions on spin 4-manifolds

2010/10/31 by Changtao Xue, Xue, Changtao, Ximin Liu +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.1011.0116

8 pages

arxiv created 2010/10/31 · arxiv updated 2010/11/02

Abstract

Let X be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to n(-E₈)\bigoplus mH, where H is the hyperbolic form. In this paper, we prove that for n such that n≡ 2 ~\rm mod ~4, there exists a locally linear pseudofree ℤ₂-action on X which is nonsmoothable with respect to any possible smooth structure on X.

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