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Explicit Dehn filling and Heegaard splittings

Futer, D
; 
Purcell, JS
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Journal Article
Date
2013-08-14
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math.GT
 math.GT
 math.DG
 57M50, 53A10
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http://hdl.handle.net/20.500.12613/5947
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1204.3617v3.pdf
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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 3-manifold X, and a Dehn filling whose meridian and longitude curves are longer than 2Ï€(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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International Press of Boston
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Communications in Analysis and Geometry
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