Volume 13, issue 4 (2009)

Download this article
For screen
For printing
Recent Issues

Volume 18 (2014)
Issue 1 1–616
Issue 2 617–1244
Issue 3 1245–1863

Volume 17 (2013) 1–5

Volume 16 (2012) 1–4

Volume 15 (2011) 1–4

Volume 14 (2010) 1–5

Volume 13 (2009) 1–5

Volume 12 (2008) 1–5

Volume 11 (2007)

Volume 10 (2006)

Volume 9 (2005)

Volume 8 (2004)

Volume 7 (2003)

Volume 6 (2002)

Volume 5 (2001)

Volume 4 (2000)

Volume 3 (1999)

Volume 2 (1998)

Volume 1 (1997)

G&T Monographs
The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index
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

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
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