Published June 2013
| Submitted
Journal Article
Open
Criterion for Cannon's Conjecture
- Creators
- Markovic, Vladimir
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.
Additional Information
© 2013 Springer Basel. Received: May 28, 2012; Revised: December 30, 2012; Accepted: January 7, 2013. Published online April 9, 2013. Vladimir Markovic is supported by the NSF Grant Number DMS-1201463. Ian Agol suggested independently that Theorem 1.1 should be true. In fact, I am grateful to Ian for reading this manuscript and sending me detailed comments that have improved the paper. Also, I would very much like to thank Leonid Potyagailo and Victor Gerasimov for sending me suggestions and corrections. My sincere thanks go to the referee for her/his numerous suggestions and comments that have greatly improved the exposition.Attached Files
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Additional details
- Eprint ID
- 39334
- Resolver ID
- CaltechAUTHORS:20130712-090917049
- DMS-1201463
- NSF
- Created
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2013-07-15Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field