## Geometry Seminar - Abstracts

### Talk

Wednesday 1 February 2017, 16:00 - 17:00 in HG03.085

**Paolo Antonini** (SISSA Trieste)

*Integrable lifts and quotients for transitive Lie algebroids*

### Abstract

In this seminar we report on work in progress with Iakovos Androulidakis and
Ioan Marcut concerning the integrability problem of 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 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).
The first part of the talk 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
an important non integrable example given by Molino.

In the last part we will explain our ideas of "removing" the obstructions of a
transitive algebroid, passing to a suitable extension or quotient.
In these cases one could still perform some of the basic constructions in
index theory and non commutative geometry.

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