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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Heegaard diagrams of $ 3$-manifolds


Author: Mitsuyuki Ochiai
Journal: Trans. Amer. Math. Soc. 328 (1991), 863-879
MSC: Primary 57N10; Secondary 57M25
MathSciNet review: 1020041
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Abstract: For a $ 3$-manifold $ M(L)$ obtained by an integral Dehn surgery along an $ n$-bridge link $ L$ with $ n$-components we define a concept of planar Heegaard diagrams of $ M(L)$ using a link diagram of $ L$. Then by using Homma-Ochiai-Takahashi's theorem and a planar Heegaard diagram of $ M(L)$ we will completely determine if $ M(L)$ is the standard $ 3$-sphere in the case when $ L$ is a $ 2$-bridge link with $ 2$-components.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1020041-2
PII: S 0002-9947(1991)1020041-2
Keywords: $ 3$-manifolds, Dehn surgery, $ n$-bridge link, Heegaard diagram
Article copyright: © Copyright 1991 American Mathematical Society