Geometry & Topology, Vol. 8 (2004) Paper no. 22, pages 831--876.

Heegaard splittings of graph manifolds

Jennifer Schultens

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

AMS subject classification. Primary: 57N10. Secondary: 57N25.

DOI: 10.2140/gt.2004.8.831

E-print: arXiv:math.GT/0406197

Submitted to GT on 30 June 2003. (Revised 1 June 2004.) Paper accepted 23 May 2004. Paper published 2 June 2004.

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Jennifer Schultens
Department of Mathematics
1 Shields Avenue
University of California
Davis, CA 95616, USA
Email: jcs@math.ucdavis.edu

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