Heegaard diagrams of 3-manifolds

Ochiai, Mitsuyuki

doi:10.1090/S0002-9947-1991-1020041-2

Heegaard diagrams of $3$-manifolds
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Trans. Amer. Math. Soc. 328 (1991), 863-879 Request permission

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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On certain sets of elements in a free group

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