Volume 13, issue 4 (2009)

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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 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 2000
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
Joel Hass
Department of Mathematics
University of California
Davis, California 95616
USA
Abigail Thompson
Department of Mathematics
University of California
Davis, California 95616
USA
William Thurston
Department of Mathematics
Cornell University
Ithaca, NY 14853
USA