|
|||||
|
|
|
|
|
|
|
|
|
Hyperbolic extensions of
free groups
Spencer Dowdall and Samuel J Taylor |
|
Geometry & Topology 22 (2018) 517–570
|
Abstract |
|
Given a finitely generated subgroup of the outer automorphism group of the rank- free group , there is a corresponding free group extension . We give sufficient conditions for when the extension is hyperbolic. In particular, we show that if all infinite-order elements of are atoroidal and the action of on the free factor complex of has a quasi-isometric orbit map, then is hyperbolic. As an application, we produce examples of hyperbolic –extensions for which has torsion and is not virtually cyclic. The proof of our main theorem involves a detailed study of quasigeodesics in Outer space that make progress in the free factor complex. This may be of independent interest. |
Keywords
hyperbolic group extensions, $\mathrm{Out}(\mathbb{F}_n)$,
Outer space, free factor complex
|
Mathematical Subject Classification 2010
Primary: 20F28, 20F67
Secondary: 20E06, 57M07
|
References |
Publication
Received: 9 March 2016
Revised: 20 October 2016
Accepted: 23 November 2016
Published: 31 October 2017
Proposed: Walter Neumann
Seconded: Benson Farb, Bruce Kleiner
|
Authors |
| Spencer Dowdall | |
| Department of Mathematics Vanderbilt University Nashville, TN United States |
|
| Samuel J Taylor | |
| Department of Mathematics Temple University Philadelphia, PA United States |
|
|
