Speaker
Prof.
Panagiotis Batakidis
(Aristotle University of Thessaloniki)
Description
The Atiyah class is an obstruction class for the existence of various geometric structures depending on the context. The original construction of Atiyah measures the obstruction to existence of holomorphic connections on holomorphic vector bundles. Since then the class has seen many applications and generalizations ranging from representation theory to quantum field theory. We construct the Atiyah class for extensions of representations up to homotopy of Lie algebroids using both the classical and the graded geometric picture in a way that recovers the class for ordinary representations. We illustrate the results in 2-term and 3-term representations. This is joint work with Sylvain Lavau.
