Median structures on asymptotic cones and homomorphisms into mapping class groups

Author: 

Behrstock, J
Drutu, C
Sapir, M

Publication Date: 

29 October 2008

Journal: 

Proc. Lond. Math. Soc.

Last Updated: 

2019-08-13T10:45:23.123+01:00

Issue: 

3

Volume: 

102

DOI: 

10.1112/plms/pdq025

page: 

503-554

abstract: 

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).

Symplectic id: 

127297

Download URL: 

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article