Geometry & Topology

Heegaard splittings of graph manifolds

Jennifer Schultens

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Abstract

Let M be a totally orientable graph manifold with characteristic submanifold T and let M=VSW 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.

Article information

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

Dates
Received: 30 June 2003
Revised: 1 June 2004
Accepted: 23 May 2004
First available in Project Euclid: 21 December 2017

Permanent link to this document
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
Primary: 57N10: Topology of general 3-manifolds [See also 57Mxx]
Secondary: 57N25: Shapes [See also 54C56, 55P55, 55Q07]

Keywords
Graph manifolds Heegaard splitting horizontal vertical

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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