Stabilization of Heegaard splittings

Joel Hass; Abigail Thompson; William Thurston

doi:10.2140/gt.2009.13.2029

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Home > Journals > Geom. Topol. > Volume 13 > Issue 4 > Article

2009 Stabilization of Heegaard splittings

Joel Hass, Abigail Thompson, William Thurston

Geom. Topol. 13(4): 2029-2050 (2009). DOI: 10.2140/gt.2009.13.2029

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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.

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Joel Hass. Abigail Thompson. William Thurston. "Stabilization of Heegaard splittings." Geom. Topol. 13 (4) 2029 - 2050, 2009. https://doi.org/10.2140/gt.2009.13.2029