Stabilizations of Heegaard splittings of graph manifolds

Ryan Derby-Talbot

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arXiv · math/0604116

Stabilizations of Heegaard splittings of graph manifolds

Ryan Derby-Talbot

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Abstract

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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Ryan Derby-Talbot. 2006-04-05. Stabilizations of Heegaard splittings of graph manifolds. https://arxiv.org/abs/math/0604116

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