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Heegaard splittings of the pair of solid torus and the core loop.

Chuichiro Hayashi, Koya Shimokawa (2001)

Revista Matemática Complutense

We show that any Heegaard splitting of the pair of the solid torus (≅D2xS1) and its core loop (an interior point xS1) is standard, using the notion of Heegaard splittings of pairs of 3-manifolds and properly imbedded graphs, which is defined in this paper.

Homology lens spaces and Dehn surgery on homology spheres

Craig Guilbault (1994)

Fundamenta Mathematicae

A homology lens space is a closed 3-manifold with ℤ-homology groups isomorphic to those of a lens space. A useful theorem found in [Fu] states that a homology lens space M 3 may be obtained by an (n/1)-Dehn surgery on a homology 3-sphere if and only if the linking form of M 3 is equivalent to (1/n). In this note we generalize this result to cover all homology lens spaces, and in the process offer an alternative proof based on classical 3-manifold techniques.

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