Continuous cohomology of contact vector fields

par M. Anastasis Fotiadis

lundi 18 mai 2026, 10:30 → 11:25 Europe/Paris

Fokko du Cloux (ICJ)

In this talk, we discuss the continuous cohomology of the Lie algebra of contact vector fields. In particular, we will prove the vanishing of the second cohomology group, providing 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.