Algebraic Ending Laminations and Quasiconvexity

Abstract

We explicate a number of notions of algebraic laminations existing in the literature, particularly in the context of an exact sequence $$1\to H\to G\to Q\to 1$$ of hyperbolic groups. These laminations arise in different contexts: existence of Cannon-Thurston maps; closed geodesics exiting ends of manifolds; dual to actions on $\mathbb{R}-$trees. We use the relationship between these laminations to prove quasiconvexity results for finitely generated infinite index subgroups of $H$, the normal subgroup in the exact sequence above.

Final version incorporating referee comments. 26 pgs 1 fig

References in corpus (2)

• Hyperbolic extensions of free groups
• The co-surface graph and the geometry of hyperbolic free group extensions

Cited by in corpus (5)

• The co-surface graph and the geometry of hyperbolic free group extensions
• Regluing graphs of Free Groups
• Trees, dendrites, and the Cannon-Thurston map
• Pullbacks of metric bundles and Cannon-Thurston maps
• Cubulating Drilled bundles over graphs