The graph structure of graph groups that are subgroups of Thompson's group V

2016/03/28 by Nathan Corwin, Corwin, Nathan, Kathryn Haymaker +1
Mathematics · #20F65 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20F65

paper · pdf · doi:10.48550/arxiv.1603.08433

arxiv created 2016/03/28 · openalex publication_date 2016/03/28 · arxiv updated 2016/03/29 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We determine exactly which graph products, also known as Right Angled Artin Groups, embed into Richard Thompson's group V. It was shown by Bleak and Salazar-Diaz that ℤ² * ℤ was an obstruction. We show that this is the only obstruction. This is shown by proving a graph theory result giving an alternate description of simple graphs without an appropriate induced subgraph.

Related

• Generalising some results about right-angled Artin groups to graph products of groups
• Embedding problem between right-angled Artin groups
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• Geometry and combinatorics via right-angled Artin groups