Handlebodies in 3-manifolds

Smythe, N.

doi:10.1090/S0002-9939-1970-0264645-5

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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