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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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