Algebraic ending laminations and quasiconvexity

Mj, Mahan; Rafi, Kasra

doi:10.2140/agt.2018.18.1883

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Algebraic ending laminations and quasiconvexity

Mahan Mj and Kasra Rafi

Algebraic & Geometric Topology 18 (2018) 1883–1916

DOI: 10.2140/agt.2018.18.1883

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.

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

Volume 18, issue 4 (2018)