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Proceedings of the American Mathematical Society

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

 

 

Handlebody complements in the $ 3$-sphere: a remark on a theorem of Fox


Author: Martin Scharlemann
Journal: Proc. Amer. Math. Soc. 115 (1992), 1115-1117
MSC: Primary 57M25; Secondary 57Q35, 57R40
MathSciNet review: 1116272
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1116272-X
Article copyright: © Copyright 1992 American Mathematical Society