Explicit Dehn filling and Heegaard splittings

David Futer; Jessica S. Purcell

doi:10.4310/cag.2013.v21.n3.a7

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arXiv · 1204.3617

Explicit Dehn filling and Heegaard splittings

David Futer·Jessica S. Purcell

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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.

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BibTeX RIS

David Futer, Jessica S. Purcell. 2013-02-25. Explicit Dehn filling and Heegaard splittings. https://doi.org/10.4310/cag.2013.v21.n3.a7

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