Unknotted solid tori and genus one Whitehead manifolds
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- by Edward M. Brown PDF
- Trans. Amer. Math. Soc. 333 (1992), 835-847 Request permission
Abstract:
In this paper we study contractible open $3$-manifolds which are monotone unions of solid tori and which embed in a compact $3$-manifold. We show that the tori are unknotted in later tori. We then study pairs of unknotted solid tori, and prove a unique prime decomposition theorem. This is applied to the open $3$-manifolds above to get an essentially unique prime decomposition. A number of examples in the literature are analyzed, and some new examples are constructed.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 333 (1992), 835-847
- MSC: Primary 57N10; Secondary 57M40
- DOI: https://doi.org/10.1090/S0002-9947-1992-1120774-4
- MathSciNet review: 1120774