Heegaard splittings of graph manifolds

Details Heegaard splittings of graph manifolds Heegaard splittings of graph manifolds

2004-06-09

arxiv.org/abs/math/0406197v2

Geom. Topol. 8(2004) 831-876

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol8/paper22.abs.html Version 2: reference [24] co

Scientific paper

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.

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