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15 October 2018 Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds
Tobias Holck Colding, David Gabai
Duke Math. J. 167(15): 2793-2832 (15 October 2018). DOI: 10.1215/00127094-2018-0022

Abstract

The main result is a short effective proof of Tao Li’s theorem that a closed non-Haken hyperbolic 3-manifold N has at most finitely many irreducible Heegaard splittings. Along the way we show that N has finitely many branched surfaces of pinched negative sectional curvature carrying all closed index-1 minimal surfaces. This effective result, together with the sequel with Daniel Ketover, solves the classification problem for Heegaard splittings of non-Haken hyperbolic 3-manifolds.

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Tobias Holck Colding. David Gabai. "Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds." Duke Math. J. 167 (15) 2793 - 2832, 15 October 2018. https://doi.org/10.1215/00127094-2018-0022

Information

Received: 4 October 2015; Revised: 10 January 2018; Published: 15 October 2018
First available in Project Euclid: 3 October 2018

zbMATH: 06982207
MathSciNet: MR3865652
Digital Object Identifier: 10.1215/00127094-2018-0022

Subjects:
Primary: 57M50

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 15 • 15 October 2018
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