Communications in Analysis and Geometry
Volume 21 (2013)
Explicit Dehn filling and Heegaard splittings
Pages: 625 – 650
We prove an explicit, quantitative criterion that ensures the Heegaard surfaces in Dehn fillings behave “as expected.” Given a cusped hyperbolic 3-manifold $X$, and a Dehn filling whose meridian and longitude curves are longer than $2π(2g − 1)$, 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.