Joint OU-OSU Geometry and Topology Seminar
Stabilizing and flipping Heeegaard splittings
Jesse Johnson, Yale University
Details
Wednesday April 2, 2008
420 Mathematics Sciences, OSU (Stillwater)
4:30 pm
Abstract
Every Heegaard splitting of a closed 3-manifold has a stabilization such that there is an isotopy of the 3-manifold that interchanges the handlebodies. I will describe a combinatorial proof that for high distance Heegaard splittings, the genus of the smallest such stabilization is bounded below by the smaller of twice the genus or half the Hempel distance of the original splitting. Similar methods imply that for certain 3-manifolds with boundary, there are pairs of Heegaard surfaces for which the minimal genus of a common stabilization is very high. The proof is inspired by the recent paper by Hass, Thompson and Thurston, which proves similar results using hyperbolic geometry, but without a precise bound in terms of the Hempel distance of the Heegaard splitting.