Heegaard splittings of graph manifolds

Schultens, Jennifer

doi:10.2140/gt.2004.8.831

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Heegaard splittings of graph manifolds

Jennifer Schultens

Geometry & Topology 8 (2004) 831–876

DOI: 10.2140/gt.2004.8.831

arXiv: math.GT/0406197

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

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

Volume 8, issue 2 (2004)