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Algebraic ending laminations and quasiconvexity

Mahan Mj and Kasra Rafi

Algebraic & Geometric Topology 18 (2018) 1883–1916
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.

Keywords
hyperbolic group, mapping torus, quasiconvexity, ending lamination, Cannon-Thurston map
Mathematical Subject Classification 2010
Primary: 20F65, 20F67
Secondary: 30F60
References
Publication
Received: 24 October 2015
Revised: 13 December 2017
Accepted: 24 February 2018
Published: 26 April 2018
Authors
Mahan Mj
School of Mathematics
Tata Institute of Fundamental Research
Mumbai
India
Kasra Rafi
Department of Mathematics
University of Toronto
Toronto, ON
Canada