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

Nathan Corwin; Kathryn Haymaker

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arXiv · 1603.08433

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

Nathan Corwin·Kathryn Haymaker

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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 $\mathbb{Z}^2 * \mathbb{Z}$ 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.

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Nathan Corwin, Kathryn Haymaker. 2016-03-28. The graph structure of graph groups that are subgroups of Thompson's group $V$. https://arxiv.org/abs/1603.08433

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