Stabilization of Heegaard splittings

Hass, Joel; Thompson, Abigail; Thurston, William

doi:10.2140/gt.2009.13.2029

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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 $g \geq 2$ 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

Volume 13, issue 4 (2009)