Circle actions and fundamental groups for homology 4-spheres

Plotnick, Steven

doi:10.1090/S0002-9947-1982-0664051-8

Circle actions and fundamental groups for homology $4$-spheres
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by Steven Plotnick

Trans. Amer. Math. Soc. 273 (1982), 393-404

DOI: https://doi.org/10.1090/S0002-9947-1982-0664051-8

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Abstract:

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

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