Explicit Dehn filling and Heegaard splittings
arXiv:1204.3617 · doi:10.4310/CAG.2013.v21.n3.a7
Abstract
We prove an explicit, quantitative criterion that ensures the Heegaard surfaces in Dehn fillings behave "as expected." Given a cusped hyperbolic manifold X, and a Dehn filling whose meridian and longitude curves are longer than 2pi(2g-1), we show that every genus g Heegaard splitting of the filled manifold is isotopic to a splitting of the original manifold X. The analogous statement holds for fillings of multiple boundary tori. This gives an effective version of a theorem of Moriah-Rubinstein and Rieck-Sedgwick.
17 pages. v3 contains minor revisions and cleaner arguments, incorporating referee comments. To appear in Communications in Analysis and Geometry