Criterion for Cannon’s Conjecture

@article{Markovi2012CriterionFC,
  title={Criterion for Cannon’s Conjecture},
  author={Vladimir Markovi{\'c}},
  journal={Geometric and Functional Analysis},
  year={2012},
  volume={23},
  pages={1035-1061}
}
  • V. Marković
  • Published 25 May 2012
  • Mathematics
  • Geometric and Functional Analysis
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… 
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