Joel Hass, Abigail Thompson, William Thurston
Published 2008-02-15, updated 2008-03-06Version 2
For each g greater than one 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. Control of families of Heegaard surfaces is obtained through a deformation to harmonic maps.
Heegaard splittings of sufficiently complicated 3-manifolds I: Stabilization
Heegaard splittings of 3--manifolds (Haifa 2005): Problems
Heegaard surfaces and measured laminations, I: the Waldhausen conjecture
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