Right-angled Artin groups and Out(F_n) I: quasi-isometric embeddings

2013/03/27 by Samuel J. Taylor, Taylor, Samuel J.
Mathematics · #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1303.6889

openalex publication_date 2013/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct quasi-isometric embeddings from right-angled Artin groups into the outer automorphism group of a free group. These homomorphisms are in analogy with those constructed in \citeCLM, where the target group is the mapping class group of a surface. Toward this goal, we develop tools in the free group setting that mirror those for surface groups as well as discuss various analogs of subsurface projection; these may be of independent interest.

Related

• The geometry of right angled Artin subgroups of mapping class groups
• Embeddings of right-angled Artin groups
• Quasi-isometry classification of right-angled Artin groups II: several infinite out cases
• Embedding problem between right-angled Artin groups
• Embedability of right-angled Artin groups into hierarchically hyperbolic groups