Duke Mathematical Journal
- Duke Math. J.
- Volume 167, Number 15 (2018), 2793-2832.
Effective finiteness of irreducible Heegaard splittings of non-Haken -manifolds
The main result is a short effective proof of Tao Li’s theorem that a closed non-Haken hyperbolic -manifold has at most finitely many irreducible Heegaard splittings. Along the way we show that has finitely many branched surfaces of pinched negative sectional curvature carrying all closed index- minimal surfaces. This effective result, together with the sequel with Daniel Ketover, solves the classification problem for Heegaard splittings of non-Haken hyperbolic -manifolds.
Duke Math. J., Volume 167, Number 15 (2018), 2793-2832.
Received: 4 October 2015
Revised: 10 January 2018
First available in Project Euclid: 3 October 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
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