## Geometry & Topology

### Stabilization of Heegaard splittings

#### Abstract

For each $g≥2$ there is a $3$–manifold with two genus–$g$ Heegaard splittings that require $g$ stabilizations to become equivalent. Previously known examples required at most one stabilization before becoming equivalent. Control of families of Heegaard surfaces is obtained through a deformation to harmonic maps.

#### Article information

Source
Geom. Topol., Volume 13, Number 4 (2009), 2029-2050.

Dates
Revised: 9 February 2009
Accepted: 17 January 2009
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513800287

Digital Object Identifier
doi:10.2140/gt.2009.13.2029

Mathematical Reviews number (MathSciNet)
MR2507114

Zentralblatt MATH identifier
1177.57018

#### Citation

Hass, Joel; Thompson, Abigail; Thurston, William. Stabilization of Heegaard splittings. Geom. Topol. 13 (2009), no. 4, 2029--2050. doi:10.2140/gt.2009.13.2029. https://projecteuclid.org/euclid.gt/1513800287

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