Journal title
Geometric and Functional Analysis
DOI
10.1007/s00039-013-0228-5
Issue
3
Volume
23
Last updated
2023-12-19T16:47:30.543+00:00
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
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Publication type
Journal Article
Publication date
01 Jun 2013