Heegaard Splittings of Boundary Reducible 3-Manifolds

2004/09/26 by Jiming Ma, Ma, Jiming, Ruifeng Qiu +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.math/0409498

12 pages, 4 figures

arxiv created 2004/09/26 · arxiv updated 2009/12/01

Abstract

In this paper, we shall prove that any Heegaard splitting of a ∂-reducible 3-manifold M, say M=W∪ V, can be obtained by doing connected sums, boundary connected sums and self-boundary connected sums from Heegaard splittings of n manifolds M₁,..., M_n where M_i is either a solid torus or a ∂-irreducible manifold. Furthermore, W∪ V is stabilized if and only if one of the factors is stabilized.

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