#### Volume 8, issue 2 (2004)

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Heegaard splittings of graph manifolds

### Jennifer Schultens

Geometry & Topology 8 (2004) 831–876
 arXiv: math.GT/0406197
##### Abstract

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

##### Keywords
Graph manifolds, Heegaard splitting, horizontal, vertical
Primary: 57N10
Secondary: 57N25
##### Publication
Revised: 1 June 2004
Accepted: 23 May 2004
Published: 2 June 2004
Proposed: Cameron Gordon
Seconded: Joan Birman, Wolfgang Metzler
##### Authors
 Jennifer Schultens Department of Mathematics 1 Shields Avenue University of California Davis California 95616 USA