3-manifolds that are sums of solid tori and Seifert fiber spaces

Heil, Wolfgang

doi:10.1090/S0002-9939-1973-0356055-X

$3$-manifolds that are sums of solid tori and Seifert fiber spaces
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by Wolfgang Heil PDF

Proc. Amer. Math. Soc. 37 (1973), 609-614 Request permission

Abstract:

It is shown that a simply connected 3-manifold is ${S^3}$ if it is a sum of a Seifert fiber space and solid tori. Let F be an orientable Seifert fiber space with a disk as orbit surface. It is shown that a sum of F and a solid torus is a Seifert fiber space or a connected sum of lens spaces. Let M be a closed 3-manifold which is a union of three solid tori. It is shown that M is a Seifert fiber space or the connected sum of two lens spaces (including ${S^1} \times {S^2}$).

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