Heegaard Splittings of Boundary Reducible 3-Manifolds

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.

12 pages, 4 figures