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 ∪_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 S_i of these strongly irreducible Heegaard splittings have the property that for each vertex manifold N of M, S_i∩N is either horizontal, pseudohorizontal, vertical or pseudovertical.

Keywords

Graph manifolds, Heegaard splitting, horizontal, vertical

Mathematical Subject Classification

Primary: 57N10

Secondary: 57N25

References

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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