The Atiyah class and ideal systems

Abstract

This talk describes the Atiyah class of a holomorphic vector bundle and explains how it can be understood as the Atiyah class of an infinitesimal ideal system. Then it explains how Molino's Atiyah class also fits in this context. The Atiyah class of a Lie pair is an obstruction to the existence of an ideal system (à la Mackenzie and Higgins) on the Lie pair.