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 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, SiN is either horizontal, pseudohorizontal, vertical or pseudovertical.

Keywords
Graph manifolds, Heegaard splitting, horizontal, vertical
Mathematical Subject Classification 2000
Primary: 57N10
Secondary: 57N25
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Publication
Received: 30 June 2003
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