Heegaard splittings of graph manifolds
Abstract
Let M be a totally orientable graph manifold with characteristic submanifold T and let M = V cupS W be a Heegaard splitting. We prove that S is standard. In particular, S is the amalgamation of strongly irreducible Heegaard splittings. The splitting surfaces Si of these strongly irreducible Heegaard splittings have the property that for each vertex manifold N of M, Si cap N is either horizontal, pseudohorizontal, vertical or pseudovertical.
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