Geometry & Topology

Stabilization of Heegaard splittings

Joel Hass, Abigail Thompson, and William Thurston

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

harmonic map Heegaard splitting stabilization isoperimetric inequality


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.

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