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Proceedings of the American Mathematical Society

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

 
 

 

Handlebodies in $ 3$-manifolds


Author: N. Smythe
Journal: Proc. Amer. Math. Soc. 26 (1970), 534-538
MSC: Primary 55.60; Secondary 57.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0264645-5
MathSciNet review: 0264645
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Abstract: Consider a knot, link or wedge of circles which bounds a singular surface of genus $ g \geqq 0$ within an orientable $ 3$-manifold. Then there is a handlebody in the manifold within which the $ 1$-complex bounds a singular surface of genus $ g$. In particular, a handlebody which is contractible in an orientable $ 3$-manifold is contractible within another handlebody.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0264645-5
Keywords: Handlebody, knot, link, singular surface, double curve, triple point, branch point, Poincaré conjecture, incompressible surface, $ n$-splitting, isotopy of links
Article copyright: © Copyright 1970 American Mathematical Society

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