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 actions by rank two finite abelian groups are homeomorphic to connected sums of CP^2, -CP^2, and S^2 x S^2 (with one exception: pseudofree Z_3 x Z_3 actions on the Chern manifold), and also establish an equivariant decompostion theorem. This generalizes results from a 1970 paper by Orlik and Raymond, 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.