On Z_3-Actions on Spin 4-Manifolds

Let X be a closed, simply-connected, smooth, spin 4-manifold whose intersection form is isomorphic to 2 k(-E_8)⊕lH, where H is the hyperbolic form. In this paper, the authors prove that if there exists a locally linear pseudofree Z_3-action on X,then Sign(g, X) ≡-k mod 3. They also investigate the smoothability of locally linear Z_3-action satisfying above congruence. In particular, it is proved that there exist some nonsmoothable locally linear Z_3-actions on certain elliptic surfaces.