On spin Z/2(p)-actions on spin 4-manifolds

Abstract

Let X be a smooth, closed, connected spin 4-manifold with b(1)(X) = 0. Assume that tau : X --> X generates a smooth Z/2(P)-action that is spin and of even type. In this article we show that under some non-degeneracy conditions the following inequality between the positive part b(2)(+)(X) of the second Betti number and the signature sigma(X) of X holds: b(2)(+)(X) greater than or equal to \ sigma(X)\/8 + p + 1. As an application, we will give classifications of spin, even Z/4-actions on homotopy K3, S-2 x S-2, K3#S-2 x S-2, and K3#K3 surfaces. (C) 2000 Elsevier Science B.V. All rights reserved.