Criterion for Cannon's Conjecture

Author: 

Markovic, V

Publication Date: 

1 June 2013

Journal: 

Geometric and Functional Analysis

Last Updated: 

2021-01-10T14:19:08.2+00:00

Issue: 

3

Volume: 

23

DOI: 

10.1007/s00039-013-0228-5

page: 

1035-1061

abstract: 

The Cannon Conjecture from the geometric group theory asserts that a word hyperbolic group that acts effectively on its boundary, and whose boundary is homeomorphic to the 2-sphere, is isomorphic to a Kleinian group. We prove the following Criterion for Cannon's Conjecture: a hyperbolic group G (that acts effectively on its boundary) whose boundary is homeomorphic to the 2-sphere is isomorphic to a Kleinian group if and only if every two points in the boundary of G are separated by a quasi-convex surface subgroup. Thus, the Cannon's conjecture is reduced to showing that such a group contains "enough" quasi-convex surface subgroups. © 2013 Springer Basel.

Symplectic id: 

1109991

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article