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    Cusp areas of farey manifolds and applications to knot theory

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    Genre
    Journal Article
    Date
    2010-12-06
    Author
    Futer, D
    Kalfagianni, E
    Purcell, JS
    Subject
    math.GT
    math.GT
    57M25, 57M27, 57M50
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/6058
    
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    DOI
    10.1093/imrn/rnq037
    Abstract
    This paper gives the first explicit, two-sided estimates on the cusp area of once-punctured-torus bundles, 4-punctured sphere bundles, and two-bridge link complements. The input for these estimates is purely combinatorial data coming from the Farey tessellation of the hyperbolic plane. The bounds on cusp area lead to explicit bounds on the volume of Dehn fillings of these manifolds, for example, sharp bounds on volumes of hyperbolic closed 3-braids in terms of the Schreier normal form of the associated braid word. Finally, these results are applied to derive relations between the Jones polynomial and the volume of hyperbolic knots, and to disprove a related conjecture. The Author 2010. Published by Oxford University Press. All rights reserved. © The Author 2010. Published by Oxford University Press. All rights reserved.
    Citation to related work
    Oxford University Press (OUP)
    Has part
    International Mathematics Research Notices
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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/6040
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