Circle actions and fundamental groups for homology 4-spheres

Abstract

We generalize work of Fintushel and Pao to give a topological classification of smooth circle actions on oriented 4 4 -manifolds Σ \Sigma satisfying H 1 ( Σ ) = 0 {H_1}(\Sigma ) = 0 . We then use these ideas to construct infinite families of homology 4 4 -spheres that do not admit effective circle actions, and whose fundamental groups cannot be 3 3 -manifold groups.