Configuration Spaces of Colored Graphs

TL;DR

This paper explores the construction of configuration spaces of colored graphs, providing concrete examples that illustrate concepts like group splittings and non-positively curved cube complexes, with applications discussed in the context of geometric group theory.

Contribution

It introduces a family of configuration space examples of colored graphs, which are not well-known but are relevant to various topics in geometric group theory.

Findings

Examples of configuration spaces of colored graphs are provided.

Applications to group splittings and cube complexes are discussed.

The paper highlights the relevance of these examples in different mathematical contexts.

Abstract

This paper is intended to provide concrete examples of concepts discussed elsewhere in this volume, especially splittings of groups and non-positively curved cube complexes but also other things. The idea of the construction (configuration spaces) is not new, but this family of examples doesn't seem to be well-known. Nevertheless they arise in a variety of contexts; applications are discussed in the last section. Most proofs are omitted.