On the disk complexes of weakly reducible, unstabilized Heegaard splittings of genus three I - the Structure Theorem

Jungsoo Kim

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arXiv · 1412.2228

On the disk complexes of weakly reducible, unstabilized Heegaard splittings of genus three I - the Structure Theorem

Jungsoo Kim

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Abstract

Let (V,W;F) be a weakly reducible, unstabilized, genus three Heegaard splitting in an orientable, irreducible 3-manifold M and DVW(F) the subset of the disk complex D(F) consisting of simplices having at least one vertex from V and at least one vertex from W. In this article, we describe the shape of DVW(F) and prove that there is a function from the components of DVW(F) to the isotopy classes of the generalized Heegaard splittings obtained by weak reductions from (V,W;F), where this function describes how the thick levels are embedded in the relevant compression bodies.

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BibTeX RIS

Jungsoo Kim. 2014-12-06. On the disk complexes of weakly reducible, unstabilized Heegaard splittings of genus three I - the Structure Theorem. https://arxiv.org/abs/1412.2228

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