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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Handlebody complements in the $3$-sphere: a remark on a theorem of Fox
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by Martin Scharlemann PDF
Proc. Amer. Math. Soc. 115 (1992), 1115-1117 Request permission

Abstract:

Let $W$ be a compact $3$-dimensional submanifold of ${S^3}$, and $C$ be a collection of disjoint simple closed curves on $\partial W$. We give necessary and sufficient conditions (one extrinsic, one intrinsic) for $W$ to have an imbedding in ${S^3}$ so that ${S^3} - W$ is a union of handlebodies, and $C$ contains a complete collection of meridia for these handlebodies.
References
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 115 (1992), 1115-1117
  • MSC: Primary 57M25; Secondary 57Q35, 57R40
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1116272-X
  • MathSciNet review: 1116272