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    Explicit Dehn filling and Heegaard splittings

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    Genre
    Journal Article
    Date
    2013-08-14
    Author
    Futer, D
    Purcell, JS
    Subject
    math.GT
    math.GT
    math.DG
    57M50, 53A10
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/5947
    
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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 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.
    Citation to related work
    International Press of Boston
    Has part
    Communications in Analysis and Geometry
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    For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5929
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