Heegaard Splittings of Boundary Reducible 3-Manifolds

Jiming Ma; Ruifeng Qiu

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Heegaard Splittings of Boundary Reducible 3-Manifolds

Jiming Ma·Ruifeng Qiu

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Abstract

In this paper, we shall prove that any Heegaard splitting of a $\partial$-reducible 3-manifold $M$, say $M=W\cup V$, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard splittings of $n$ manifolds $M_{1},..., M_{n}$ where $M_{i}$ is either a solid torus or a $\partial$-irreducible manifold. Furthermore, $W\cup V$ is stabilized if and only if one of the factors is stabilized.

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BibTeX RIS

Jiming Ma, Ruifeng Qiu. 2004-09-26. Heegaard Splittings of Boundary Reducible 3-Manifolds. https://arxiv.org/abs/math/0409498

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