Volume 13, issue 4 (2009)

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Covers and the curve complex

Kasra Rafi and Saul Schleimer

Geometry & Topology 13 (2009) 2141–2162
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/