Median structures on asymptotic cones and homomorphisms into mapping class groups

Details Median structures on asymptotic cones and homomorphisms into mapping class groups Median structures on asymptotic cones and homomorphisms into mapping class groups

2008-10-29

arxiv.org/abs/0810.5376v4

Mathematics

Geometric Topology

final version, to appear in Proc. LMS

Scientific paper

10.1112/plms/pdq025

The main goal of this paper is a detailed study of asymptotic cones of the mapping class groups. In particular, we prove that every asymptotic cone of a mapping class group has a bi-Lipschitz equivariant embedding into a product of real trees, sending limits of hierarchy paths onto geodesics, and with image a median subspace. One of the applications is that a group with Kazhdan's property (T) can have only finitely many pairwise non-conjugate homomorphisms into a mapping class group. We also give a new proof of the rank conjecture of Brock and Farb (previously proved by Behrstock and Minsky, and independently by Hamenstaedt).

Affiliated with

Also associated with

No associations

Rating

Median structures on asymptotic cones and homomorphisms into 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 Median structures on asymptotic cones and homomorphisms into mapping class groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Median structures on asymptotic cones and homomorphisms into mapping class groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-278016