Embeddings into Thompson's groups from quasi-median geometry

Abstract

The main result of this article is that any braided (resp. annular, planar) diagram group $D$ splits as a short exact sequence $1 \to R \to D \to S \to 1$ where $R$ is a subgroup of some right-angled Artin group and $S$ a subgroup of Thompson's group $V$ (resp. $T$, $F$). As an application, we show that several braided diagram groups embed into Thompson's group $V$, including Higman's groups $V\_{n,r}$, groups of quasi-automorphisms $QV\_{n,r,p}$, and generalised Houghton's groups $H\_{n,p}$.