| Résume | Tangles are embeddings $\coprod S^1 \cup \coprod [0,1] \rightarrow \mathbb{R}^3$. If instead we embed our circles and intervals into a surface we have the notion of $v$-tangles or $w$-tangles. Building on work of Bar-Natan and Dancso we give wheeled props that capture the Reidemeister theory of $v$ and $w$ tangles. We explain how the group of homotopy automorphisms of (a weakened version of) the wheeled prop for $w$-tangles acts on the space of solutions to the Kashiwara–Vergne problem and will give some updates on ongoing work describing a conjectured relationship between this group and the Grothendieck–Teichmüller group. This talk includes pieces of joint work with Z. Dancso and I. Halacheva. |
