Heegaard Splittings of Boundary Reducible 3-Manifolds

Details Heegaard Splittings of Boundary Reducible 3-Manifolds Heegaard Splittings of Boundary Reducible 3-Manifolds

2004-09-26

arxiv.org/abs/math/0409498v1

Mathematics

Geometric Topology

12 pages, 4 figures

Scientific paper

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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