Wheeled Props, tangles and a group like GT

Seminar/Forum

Wheeled Props, tangles and a group like GT

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 Dansco we give modular operads that captures 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-Teichmuller group. This talk includes ongoing joint work with Z. Dansco and I. Halacheva.

Presenter

  • Dr Marcy Robertson
    Dr Marcy Robertson, University of Melbourne