Communications in Analysis and Geometry

Volume 21 (2013)

Number 3

Explicit Dehn filling and Heegaard splittings

Pages: 625 – 650

DOI: http://dx.doi.org/10.4310/CAG.2013.v21.n3.a7

Authors

David Futer (Department of Mathematics, Temple University, Philadelphia, Pennsylvania, U.S.A.)

Jessica S. Purcell (Department of Mathematics, Brigham Young University, Provo, Utah, U.S.A.)

Abstract

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.

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