Convex cocompact subgroups of mapping class groups

Details Convex cocompact subgroups of mapping class groups Convex cocompact subgroups of mapping class groups

2001-06-22

arxiv.org/abs/math/0106190v3

Geom. Topol. 6 (2002) 91-152

Mathematics

Group Theory

Published in Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper5.abs.html

Scientific paper

We develop a theory of convex cocompact subgroups of the mapping class group MCG of a closed, oriented surface S of genus at least 2, in terms of the action on Teichmuller space. Given a subgroup G of MCG defining an extension L_G: 1--> pi_1(S) --> L_G --> G -->1 we prove that if L_G is a word hyperbolic group then G is a convex cocompact subgroup of MCG. When G is free and convex cocompact, called a "Schottky subgroup" of MCG, the converse is true as well; a semidirect product of pi_1(S) by a free group G is therefore word hyperbolic if and only if G is a Schottky subgroup of MCG. The special case when G=Z follows from Thurston's hyperbolization theorem. Schottky subgroups exist in abundance: sufficiently high powers of any independent set of pseudo-Anosov mapping classes freely generate a Schottky subgroup.

Affiliated with

Also associated with

No associations

Rating

Convex cocompact subgroups of mapping class groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Convex cocompact subgroups of mapping class groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convex cocompact subgroups of mapping class groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-596559