| Résume | In this talk we will be concerned with smooth, framed fiber bundles whose fibers are the standard d-dimensional disk, trivialized along the boundary. "Kontsevich's characteristic classes" are invariants defined for these bundles: given such a bundle \pi:E \to B, we can associate to it a collection of cohomology classes in H^*(B). On the other hand, there is a "bracket operation" for these bundles defined by Sander Kupers: namely, given two such bundles \pi_1 and \pi_2 as input, we can output a "bracket bundle" [\pi_1,\pi_2]. I will talk about this bracket bundle construction and a formula relating the Kontsevich's classes of [\pi_1,\pi_2] with those of \pi_1 and \pi_2. The main input of the proof is a new but very natural configuration space generalizing the Fulton-MacPherson configuration spaces. This is a work in progress joint with Robin Koytcheff and Sander Kupers. |
