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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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


Author: Wolfgang Heil
Journal: Proc. Amer. Math. Soc. 37 (1973), 609-614
MSC: Primary 57A10
MathSciNet review: 0356055
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0356055-X
PII: S 0002-9939(1973)0356055-X
Keywords: Seifert fiber spaces, Dehn construction, simply connected 3-manifold
Article copyright: © Copyright 1973 American Mathematical Society