Right-angled Artin subgroups of the $C^{\infty}$ diffeomorphism group of the real line

TL;DR

This paper demonstrates that all right-angled Artin groups, along with certain other groups, can be embedded into the group of smooth diffeomorphisms of the real line, revealing new connections between group theory and smooth dynamics.

Contribution

It proves that every right-angled Artin group and related groups embed into the $C^{ abla}$ diffeomorphism group of the real line, expanding understanding of group actions on smooth manifolds.

Findings

All right-angled Artin groups embed into the $C^{ abla}$ diffeomorphism group of the real line.

Every limit group and countable residually RAAG group embed into the $C^{ abla}$ diffeomorphism group.

The result connects algebraic properties of groups with smooth dynamical systems.

Abstract

We prove that every right-angled Artin group embeds into the $C^{\infty}$ diffeomorphism group of the real line. As a corollary, we show every limit group, and more generally every countable residually RAAG group, embeds into the $C^{\infty}$ diffeomorphism group of the real line.