#### Volume 13, issue 4 (2009)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Stabilization of Heegaard splittings

### Joel Hass, Abigail Thompson and William Thurston

Geometry & Topology 13 (2009) 2029–2050
##### Abstract

For each $g\ge 2$ 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.

##### Keywords
harmonic map, Heegaard splitting, stabilization, isoperimetric inequality
Primary: 57M25
Secondary: 53C43