NCG seminar

[Emanuele Tuillier Illingworth]

*"NON-COMMUTATIVE GEOMETRY" SEMINAR 
<https://www.math.sissa.it/content/non-commutative-geometry-seminars>*

Friday 15 April 2016 at 11:30am
Venue: SISSA, Room 134

Dr. Paolo Antonini (Trieste University)
"Non-integrable Lie algebroids"

Abstract:
In this seminar we report on work in progress with Iakovos 
Androulidakis concerning the integrability problem of transitive Lie 
algebroids.

In many constructions in non-commutative geometry the passage from a 
singular space to a C*-algebra involves the use of a Lie groupoid as an 
intermediate desingularization. The infinitesimal data of a Lie groupoid 
is a Lie algebroid and in general is not possible to integrate a Lie 
algebroid to a Lie groupoid (in contrast to the theory of Lie algebras).

Lie algebroids are very common: for example foliations, Poisson 
manifolds and connections on principal bundles are described by these 
structures.

The major part of the seminar will be concerned with the discussion of 
Lie algebroids: basic definitions, examples, what does it mean 
to integrate an algebroid to a Lie groupoid, the obstructions to the 
integrability of Crainic-Fernandes and the discussion of an important 
non-integrable example given by Molino.

In the last part we will explain our idea of removing the obstructions 
of a transitive algebroid passing to a suitably good extension. In this 
case one can still perform some of the standard constructions in index 
theory and non commutative geometry.