Geometry & Topology 13 (2009) 2029–2050

DOI: 10.2140/gt.2009.13.2029

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.

Keywords

harmonic map, Heegaard splitting, stabilization, isoperimetric inequality

Mathematical Subject Classification

Primary: 57M25

Secondary: 53C43

References

Publication

Received: 22 April 2008
Revised: 9 February 2009
Accepted: 17 January 2009
Published: 26 April 2009
Proposed: Joan Birman
Seconded: Jean-Pierre Otal, Ron Stern

Authors