Strongly irreducible Heegaard splittings of hyperbolic 3-manifolds

Kalelkar, Tejas

doi:10.1090/proc/15114

Strongly irreducible Heegaard splittings of hyperbolic 3-manifolds
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by Tejas Kalelkar

Proc. Amer. Math. Soc. 148 (2020), 4527-4529

DOI: https://doi.org/10.1090/proc/15114

Published electronically: June 30, 2020

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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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