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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Unknotted solid tori and genus one Whitehead manifolds


Author: Edward M. Brown
Journal: Trans. Amer. Math. Soc. 333 (1992), 835-847
MSC: Primary 57N10; Secondary 57M40
MathSciNet review: 1120774
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1992-1120774-4
PII: S 0002-9947(1992)1120774-4
Keywords: Whitehead manifold, open $ 3$-manifold, contractible manifold
Article copyright: © Copyright 1992 American Mathematical Society