Embeddings of right-angled Artin groups into higher dimensional Thompson groups

TL;DR

This paper demonstrates how to embed right-angled Artin groups into higher dimensional Thompson groups, expanding understanding of their algebraic and geometric relationships.

Contribution

It introduces a method to embed any right-angled Artin group into an n-dimensional Thompson group based on the graph's structure.

Findings

Every right-angled Artin group can be embedded into an n-dimensional Thompson group.

The embedding depends on the number of complementary edges in the defining graph.

This work links graph properties to group embeddings in higher dimensions.

Abstract

In this paper, we construct embeddings of right-angled Artin groups into higher dimensional Thompson groups. In particular, we embed every right-angled Artin groups into n-dimensional Thompson group, where n is the number of complementary edges in the defining graph.