Duke Mathematical Journal

Effective finiteness of irreducible Heegaard splittings of non-Haken $3$-manifolds

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-$\le1$ 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.

Article information

Source
Duke Math. J., Volume 167, Number 15 (2018), 2793-2832.

Dates
Revised: 10 January 2018
First available in Project Euclid: 3 October 2018

https://projecteuclid.org/euclid.dmj/1538532049

Digital Object Identifier
doi:10.1215/00127094-2018-0022

Mathematical Reviews number (MathSciNet)
MR3865652

Zentralblatt MATH identifier
06982207

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds

Citation

Colding, Tobias Holck; Gabai, David. Effective finiteness of irreducible Heegaard splittings of non-Haken $3$ -manifolds. Duke Math. J. 167 (2018), no. 15, 2793--2832. doi:10.1215/00127094-2018-0022. https://projecteuclid.org/euclid.dmj/1538532049

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