## Geometry & Topology

### Heegaard splittings of graph manifolds

Jennifer Schultens

#### Abstract

Let $M$ be a totally orientable graph manifold with characteristic submanifold $T$ and let $M=V∪SW$ 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 $M$, $Si∩N$ is either horizontal, pseudohorizontal, vertical or pseudovertical.

#### Article information

Source
Geom. Topol., Volume 8, Number 2 (2004), 831-876.

Dates
Revised: 1 June 2004
Accepted: 23 May 2004
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513883418

Digital Object Identifier
doi:10.2140/gt.2004.8.831

Mathematical Reviews number (MathSciNet)
MR2087071

Zentralblatt MATH identifier
1055.57023

Subjects

#### Citation

Schultens, Jennifer. Heegaard splittings of graph manifolds. Geom. Topol. 8 (2004), no. 2, 831--876. doi:10.2140/gt.2004.8.831. https://projecteuclid.org/euclid.gt/1513883418

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