Duke Mathematical Journal

On the classification of Heegaard splittings

Tobias Holck Colding, David Gabai, and Daniel Ketover

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Abstract

The long-standing classification problem in the theory of Heegaard splittings of 3-manifolds is to exhibit for each closed 3-manifold a complete list, without duplication, of all its irreducible Heegaard surfaces, up to isotopy. We solve this problem for non-Haken hyperbolic 3-manifolds.

Article information

Source
Duke Math. J., Volume 167, Number 15 (2018), 2833-2856.

Dates
Received: 4 October 2015
Revised: 10 January 2018
First available in Project Euclid: 3 October 2018

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1538532048

Digital Object Identifier
doi:10.1215/00127094-2018-0023

Mathematical Reviews number (MathSciNet)
MR3865653

Zentralblatt MATH identifier
06982208

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

Keywords
Heegaard 3-manifold hyperbolic foliation sweep-out minimal surface

Citation

Colding, Tobias Holck; Gabai, David; Ketover, Daniel. On the classification of Heegaard splittings. Duke Math. J. 167 (2018), no. 15, 2833--2856. doi:10.1215/00127094-2018-0023. https://projecteuclid.org/euclid.dmj/1538532048


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