Heegaard splittings of graph manifolds

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.

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

Cited by in corpus (3)

• Topological Index Theory for Surfaces in 3-Manifolds
• The Morse-Novikov number of knots under connected sum and cabling
• The growth rate of the tunnel number of m-small knots