Linearity of fundamental groups of graphs of virtually cyclic groups

TL;DR

This paper characterizes when certain complex groups, specifically generalized Baumslag-Solitar groups and graphs of groups with virtually cyclic components, are linear, extending known results to broader classes of groups.

Contribution

It provides a characterization of linearity for generalized Baumslag-Solitar groups and extends this to fundamental groups of graphs of groups with virtually cyclic vertex and edge groups.

Findings

Generalized Baumslag-Solitar groups are linear under specific conditions.

Extended linearity criteria to graphs of groups with virtually cyclic groups.

Enhanced understanding of the structure and linearity of complex group classes.

Abstract

We characterize when a generalized Baumslag-Solitar group is linear, and extend the result to the fundamental groups of a graph of groups with infinite virtually cyclic vertex and edge groups.