Algebraic Ending Laminations and Quasiconvexity

Mahan Mj; Kasra Rafi

doi:10.2140/agt.2018.18.1883

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arXiv · 1506.08036

Algebraic Ending Laminations and Quasiconvexity

Mahan Mj·Kasra Rafi

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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 $\R-$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.

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Mahan Mj, Kasra Rafi. 2015-06-26. Algebraic Ending Laminations and Quasiconvexity. https://doi.org/10.2140/agt.2018.18.1883

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