Orateur
M.
Paolo Antonini
Description
In this seminar we report on work in progress with I. Androulidakis and I. Marcut
In many constructions in noncommutative geometry, the passage from a singular space to a C* algebra involves a Lie groupoid as an intermediate desingularization space.
The infinitesimal datum of a Lie groupoid is a Lie algebroid and they appear independently, for instance in :
-theory of foliations
-Poisson geometry
-Gauge theory.
However in general is not possible to integrate a Lie algebroid to a Lie groupoid ( in contrast to the theory of Lie algebras).
Firstly we will be concerned with the discussion of Lie algebroids: basic definitions, examples, the integration problem, the obstructions to the integrability of Crainic-Fernandes and the discussion of the first non integrable example given by Molino.
Then we will explain our idea of "removing" the obstructions of a transitive algebroid, passing to a suitable integrable extension.
In these cases one can use this integrable lift to perform some of the basic constructions of index theory and noncommutative geometry.
