Four-manifolds which admit {Z_p x Z_p} actions

Abstract

We show that the simply-connected four-manifolds which admit locally linear, homologically trivial Zp × Zp actions are homeomorphic to connected sums of ±CP 2 and S 2 × S 2 (with one exception: pseudofree Z 3 × Z 3 actions on the Chern manifold), and also establish an equivariant decomposition theorem.This generalizes results from a 1970 paper by Orlik and Raymond about torus actions, and complements more recent work of Fintushel, Yoshida, and Huck on S 1 actions.In each case, the simply-connected four-manifolds which support such actions are essentially the same.