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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Identification of certain $ 4$-manifolds with group actions


Authors: Ronald Fintushel and Peter Sie Pao
Journal: Proc. Amer. Math. Soc. 67 (1977), 344-350
MSC: Primary 57E25
DOI: https://doi.org/10.1090/S0002-9939-1977-0501042-5
MathSciNet review: 0501042
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Abstract: If $ {M^3}$ is an orientable 3-manifold with an $ {S^1}$-action or is a Seifert fiber space, then the 4-manifold obtained by surgery along singular fibers in $ M \times {S^1}$ can also be obtained by surgery in $ {V^3} \times {S^1}$, where V is a manifold related to M but with fewer singular fibers. An application is given to Scharlemann's ``exotic'' $ ({S^3} \times {S^1}\;\char93 \;{S^2} \times {S^2})$'s.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0501042-5
Article copyright: © Copyright 1977 American Mathematical Society