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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Circle actions and fundamental groups for homology $ 4$-spheres


Author: Steven Plotnick
Journal: Trans. Amer. Math. Soc. 273 (1982), 393-404
MSC: Primary 57S15; Secondary 57M99
MathSciNet review: 664051
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0664051-8
PII: S 0002-9947(1982)0664051-8
Article copyright: © Copyright 1982 American Mathematical Society