Stabilizations of Heegaard splittings of graph manifolds

Details Stabilizations of Heegaard splittings of graph manifolds Stabilizations of Heegaard splittings of graph manifolds

2006-04-05

arxiv.org/abs/math/0604116v1

Mathematics

Geometric Topology

53 pages, 37 figures

Scientific paper

We show that after one stabilization, a strongly irreducible Heegaard splitting of suitably large genus of a graph manifold is isotopic to an amalgamation along a modified version of the system of canonical tori in the JSJ decomposition. As a corollary, two strongly irreducible Heegaard splittings of a graph manifold of suitably large genus are isotopic after at most one stabilization of the higher genus splitting.

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