Covers and the curve complex

Rafi, Kasra; Schleimer, Saul

doi:10.2140/gt.2009.13.2141

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Covers and the curve complex

Kasra Rafi and Saul Schleimer

Geometry & Topology 13 (2009) 2141–2162

DOI: 10.2140/gt.2009.13.2141

Abstract

We provide the first nontrivial examples of quasi-isometric embeddings between curve complexes; these are induced by orbifold covers. This leads to new quasi-isometric embeddings between mapping class groups. As a corollary, in the mapping class group normalizers of finite subgroups are undistorted.

Keywords

mapping class group, complex of curves, cover, undistorted subgroup

Mathematical Subject Classification 2000

Primary: 57M99

Secondary: 30F99

References

Publication

Received: 27 July 2008

Revised: 17 April 2009

Accepted: 19 January 2009

Published: 5 May 2009

Proposed: Benson Farb

Seconded: Walter Neumann, Danny Calegari

Authors

Kasra Rafi
Department of Mathematics University of Chicago 5734 S University Avenue Chicago, Illinois 60637 USA
http://www.math.uchicago.edu/~rafi
Saul Schleimer
Mathematics Institute University of Warwick Coventry, CV4 7A UK
http://www.warwick.ac.uk/~masgar/

Volume 13, issue 4 (2009)