Four-Manifolds which admit Z_p x Z_p actions

Details Four-Manifolds which admit Z_p x Z_p actions Four-Manifolds which admit Z_p x Z_p actions

2000-02-22

arxiv.org/abs/math/0002187v2

Forum Mathematicum 14 (4) 2002 pp. 495--507

Mathematics

Geometric Topology

11 pages, LaTeX, 1 figure. This is a minor revision to make the paper more self-contained

Scientific paper

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.

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