On ℤ₃-actions on spin 4-manifolds

Abstract

Let X be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to 2k(−E _s) ⊕ lH, where H is the hyperbolic form. In this paper, the authors prove that if there exists a locally linear pseudofree ℤ₃-action on X, then Sign(g,X) ≡ −k mod 3. They also investigate the smoothability of locally linear ℤ₃-action satisfying above congruence. In particular, it is proved that there exist some nonsmoothable locally linear ℤ₃-actions on certain elliptic surfaces.

Keywords

Group action / Locally linear / Kirby-Siebenmann invariant / Nonsmoothable

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