Identification of certain 4-manifolds with group actions

Fintushel, Ronald; Pao, Peter Sie

doi:10.1090/S0002-9939-1977-0501042-5

Identification of certain $4$-manifolds with group actions
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by Ronald Fintushel and Peter Sie Pao PDF

Proc. Amer. Math. Soc. 67 (1977), 344-350 Request permission

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” $({S^3} \times {S^1}\;\# \;{S^2} \times {S^2})$’s.

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