Heegaard splittings of graph manifolds

Schultens, Jennifer¹

¹ Department of Mathematics, 1 Shields Avenue, University of California, Davis, California 95616, USA

Geometry & topology, Tome 8 (2004) no. 2, pp. 831-876.

Résumé

Let $M$ be a totally orientable graph manifold with characteristic submanifold $\mathcal{T}$ 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.

Détail

DOI : 10.2140/gt.2004.8.831

Keywords: Graph manifolds, Heegaard splitting, horizontal, vertical

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