## Algebraic & Geometric Topology

### 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

$1 → H → G → Q → 1$

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.

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 4 (2018), 1883-1916.

Dates
Revised: 13 December 2017
Accepted: 24 February 2018
First available in Project Euclid: 3 May 2018

https://projecteuclid.org/euclid.agt/1525312822

Digital Object Identifier
doi:10.2140/agt.2018.18.1883

Mathematical Reviews number (MathSciNet)
MR3797060

Zentralblatt MATH identifier
06867651

#### Citation

Mj, Mahan; Rafi, Kasra. Algebraic ending laminations and quasiconvexity. Algebr. Geom. Topol. 18 (2018), no. 4, 1883--1916. doi:10.2140/agt.2018.18.1883. https://projecteuclid.org/euclid.agt/1525312822

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