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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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Keywords: Whitehead manifold, open $ 3$-manifold, contractible manifold
Article copyright: © Copyright 1992 American Mathematical Society

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