Explicit Dehn filling and Heegaard splittings

Details Explicit Dehn filling and Heegaard splittings Explicit Dehn filling and Heegaard splittings

2012-04-16

arxiv.org/abs/1204.3617v2

Mathematics

Geometric Topology

16 pages. v2 contains added references and expanded exposition of past results

Scientific paper

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 comes from 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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