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The curve complex and covers via hyperbolic 3-manifolds

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Abstract

Rafi and Schleimer recently proved that the natural relation between curve complexes induced by a covering map between two surfaces is a quasi-isometric embedding. We offer another proof of this result using a distance estimate via hyperbolic 3-manifolds.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

    Robert Tang

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  1. Robert Tang
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Correspondence to Robert Tang.

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Tang, R. The curve complex and covers via hyperbolic 3-manifolds. Geom Dedicata 161, 233–237 (2012). https://doi.org/10.1007/s10711-012-9703-7

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  • DOI: https://doi.org/10.1007/s10711-012-9703-7

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