Geometry & Topology

Stabilization of Heegaard splittings

Joel Hass, Abigail Thompson, and William Thurston

Full-text: Open access

Abstract

For each g2 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
Received: 22 April 2008
Revised: 9 February 2009
Accepted: 17 January 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]

Keywords
harmonic map Heegaard splitting stabilization isoperimetric inequality

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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