2-holonomy representations via the Kontsevich integration map (Matthew Jackson)

Orateur : Matthew Jackson

Lieu : salle des Séminaires M3

Résumé :

The Knizhnik-Zamolodchikov connection is a very powerful tool in constructing representations of braid groups. We investigate a higher order version of this connection due to Komendarczyk, Koytcheff and Volic, and construct a representation of the path 2-groupoid of the configuration space of $m$ points in $\mathbb{R}^3$ via the Kontsevich integration map. We show that this representation behaves nicely with respect to compositions of homotopies. This work was done during my internship at the University of Tokyo and Meiji University under the supervision of Toshitake Kohno.