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Geometriae Dedicata

, Volume 161, Issue 1, pp 233–237 | Cite as

The curve complex and covers via hyperbolic 3-manifolds

  • Robert Tang
Original Paper

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 complex Covering spaces Hyperbolic 3-manifolds Quasi-isometric embedding 

Mathematics Subject Classification (2000)

57M50 20F65 32G15 

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References

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of WarwickCoventryUK

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