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

Let X be a smooth, closed, connected spin 4-manifold with b1(X)=0 . Assume that τ :X→X generates a smooth Z/2p -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 b2+(X) of the second Betti number and the signature σ(X) of X holds: b2+(X)≥|σ(X)|/8+p+1 . application, we will give classifications of spin, even Z/4 -actions on homotopy K3,S2×S2,K3#S2×S2 , and K3#K3 surfaces.