Strongly irreducible Heegaard splittings of hyperbolic 3-manifolds

Tejas Kalelkar

doi:10.1090/proc/15114

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arXiv · 1911.11964

Strongly irreducible Heegaard splittings of hyperbolic 3-manifolds

Tejas Kalelkar

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Abstract

Colding and Gabai have given an effective version of Li's theorem that non-Haken hyperbolic 3-manifolds have finitely many irreducible Heegaard splittings. As a corollary of their work, we show that Haken hyperbolic 3-manifolds have a finite collection of strongly irreducible Heegaard surfaces $S_i$ and incompressible surfaces $K_j$ such that any strongly irreducible Heegaard surface is a Haken sum $S_i + \sum_j n_j K_j$, up to one-sided associates of the Heegaard surfaces.

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BibTeX RIS

Tejas Kalelkar. 2019-11-27. Strongly irreducible Heegaard splittings of hyperbolic 3-manifolds. https://doi.org/10.1090/proc%2F15114

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