Algebraic & Geometric Topology

Algebraic ending laminations and quasiconvexity

Mahan Mj and 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 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 –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
Received: 24 October 2015
Revised: 13 December 2017
Accepted: 24 February 2018
First available in Project Euclid: 3 May 2018

Permanent link to this document
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

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups
Secondary: 30F60: Teichmüller theory [See also 32G15]

Keywords
hyperbolic group mapping torus quasiconvexity ending lamination Cannon-Thurston map

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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