Stabilization of Heegaard splittings

Hass, Joel¹ ; Thompson, Abigail¹ ; Thurston, William²

¹ Department of Mathematics, University of California, Davis, California 95616, USA
² Department of Mathematics, Cornell University, Ithaca, NY 14853, USA

Geometry & topology, Tome 13 (2009) no. 4, pp. 2029-2050.

Résumé

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.

Détail

DOI : 10.2140/gt.2009.13.2029

Keywords: harmonic map, Heegaard splitting, stabilization, isoperimetric inequality

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