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Algebraic ending laminations and quasiconvexity. (English) Zbl 06867651
Summary: We explicate a number of notions of algebraic laminations existing in the literature, particularly in the context of an exact sequence \[ 1\rightarrow H\rightarrow G \rightarrow Q \rightarrow 1 \] 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.

MSC:
20F65 Geometric group theory
20F67 Hyperbolic groups and nonpositively curved groups
30F60 Teichmüller theory for Riemann surfaces
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