Complexes of groups and geometric small cancellation over graphs of groups

TL;DR

This paper generalizes Gromov's construction to realize small cancellation groups over graphs of groups as fundamental groups of non-positively curved complexes, linking their hyperbolicity and finiteness properties to local groups.

Contribution

It introduces a generalized construction for small cancellation groups over graphs of groups as non-positively curved complexes, extending Gromov's original work.

Findings

Conditions for hyperbolicity of small cancellation quotients

Finiteness properties derived from local groups

Construction of non-positively curved complexes of groups

Abstract

We explain and generalise a construction due to Gromov to realise geometric small cancellation groups over graphs of groups as fundamental groups of non-positively curved 2-dimensional complexes of groups. We then give conditions so that the hyperbolicity and some finiteness properties of the small cancellation quotient can be deduced from analogous properties for the local groups of the initial graph of groups.