Covers and the curve complex

Rafi, Kasra¹ ; Schleimer, Saul²

¹ Department of Mathematics, University of Chicago, 5734 S University Avenue, Chicago, Illinois 60637, USA
² Mathematics Institute, University of Warwick, Coventry, CV4 7A, UK

Geometry & topology, Tome 13 (2009) no. 4, pp. 2141-2162.

Résumé

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.

Détail

DOI : 10.2140/gt.2009.13.2141

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

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