“Continuous cohomology of contact vector fields”
Martedì 27 Gennaio 2026, ore 17:00 - Aula 2AB40 - Anastasios Fotiadis (Université Claude Bernard - Lyon 1)
Abstract
In this talk, we prove the vanishing of the first and second continuous cohomology groups of the Lie algebra of contact vector fields. In particular, the vanishing of the second cohomology group yields a complete classification of its continuous central extensions.
We first introduce the necessary tools from the theory of locally convex spaces to explain the Frèchet structure on this Lie algebra. We then determine its cohomology via a local-to-global strategy. This is carried out in two steps: first we focus on a local model involving compactly supported vector fields and then using a gluing argument to extend the result globally.
This is joint work with Bas Janssens, Cornelia Vizman and Stefan Haller.
