Strong accessibility for finitely presented groups

Louder, Larsen; Touikan, Nicholas

doi:10.2140/gt.2017.21.1805

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Strong accessibility for finitely presented groups

Larsen Louder and Nicholas Touikan

Geometry & Topology 21 (2017) 1805–1835

DOI: 10.2140/gt.2017.21.1805

Abstract

A hierarchy of a group is a rooted tree of groups obtained by iteratively passing to vertex groups of graphs of groups decompositions. We define a (relative) slender JSJ hierarchy for (almost) finitely presented groups and show that it is finite, provided the group in question doesn’t contain any slender subgroups with infinite dihedral quotients and satisfies an ascending chain condition on certain chains of subgroups of edge groups.

As a corollary, slender JSJ hierarchies of finitely presented subgroups of ${SL}_{n} (ℤ)$ or of hyperbolic groups which are (virtually) without $2$ –torsion are finite.

Keywords

strong accessibility, graph of groups, hierarchy

Mathematical Subject Classification 2010

Primary: 20E08, 20F65, 20F67, 57M60

References

Publication

Received: 22 September 2015

Accepted: 5 April 2016

Published: 10 May 2017

Proposed: Benson Farb

Seconded: Dmitri Burago, Danny Calegari

Authors

Larsen Louder
Department of Mathematics University College London Gower Street London WC1E 6BT United Kingdom

Nicholas Touikan
Department of Mathematical Sciences Stevens Institute of Technology 1 Castle Point on Hudson Hoboken, NJ 07030 United States

Volume 21, issue 3 (2017)