On local tameness of certain graphs of groups

Gitik, Rita

doi:10.2140/agt.2019.19.3701

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On local tameness of certain graphs of groups

Rita Gitik

Algebraic & Geometric Topology 19 (2019) 3701–3710

DOI: 10.2140/agt.2019.19.3701

Abstract

Let $G$ be the fundamental group of a finite graph of groups with Noetherian edge groups and locally tame vertex groups. We prove that $G$ is locally tame. It follows that if a finitely presented group $H$ has a nontrivial $JSJ$ –decomposition over the class of its $VPC (k)$ subgroups for $k = 1$ or $k = 2$ , and all the vertex groups in the decomposition are flexible, then $H$ is locally tame.

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Keywords

Noetherian group, locally tame group, graph of groups, \JSJ–decomposition, covering space, fundamental group

Mathematical Subject Classification 2010

Primary: 20F65

Secondary: 20E06, 20F34, 57M07, 57M10

References

Publication

Received: 29 August 2018

Revised: 28 November 2018

Accepted: 11 May 2019

Published: 17 December 2019

Authors

Rita Gitik
Department of Mathematics University of Michigan Ann Arbor, MI United States

Volume 19, issue 7 (2019)