#### Geometry & Topology, Vol. 8 (2004)
Paper no. 22, pages 831--876.

## Heegaard splittings of graph manifolds

### Jennifer Schultens

**Abstract**.
Let M be a totally orientable graph manifold with characteristic
submanifold 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

**AMS subject classification**.
Primary: 57N10.
Secondary: 57N25.

**DOI:** 10.2140/gt.2004.8.831

**E-print:** `arXiv:math.GT/0406197`

Submitted to GT on 30 June 2003.
(Revised 1 June 2004.)
Paper accepted 23 May 2004.
Paper published 2 June 2004.

Notes on file formats
Jennifer Schultens

Department of Mathematics

1 Shields Avenue

University of California

Davis, CA 95616, USA

Email: jcs@math.ucdavis.edu

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