Geometriae Dedicata

, Volume 161, Issue 1, pp 233–237

The curve complex and covers via hyperbolic 3-manifolds

Original Paper

DOI: 10.1007/s10711-012-9703-7

Cite this article as:
Tang, R. Geom Dedicata (2012) 161: 233. doi:10.1007/s10711-012-9703-7
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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.

Keywords

Curve complexCovering spacesHyperbolic 3-manifoldsQuasi-isometric embedding

Mathematics Subject Classification (2000)

57M5020F6532G15

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK