## MAT 1341F Topics in Differential Geometry: Lie Groupoids and Lie Algebroids

**Classes:**
M10-12, T2 BA 6180

Lie groupoids, and their infinitesimal counterparts, the Lie algebroids, arise in many areas of differential geometry, such a Poisson geometry, index theory, foliation theory, or symmetries of differential equations. In recent years, there has been a lot of progress towards understanding these structures, such as the Crainic-Fernandes integrability obstructions and various results on 'multiplicative structures' on Lie groupoids.
Tentative topics include:

- Lie groupoids: Definitions, examples, basic properties
- Lie algebroids: Definitions, examples, basic properties
- The Crainic-Fernandes integration theorem
- Cohomology of Lie groupods and Lie algebroids, van Est map
- Double structures (?)
- The algebra associated to a Lie groupoid (?)

Prerequisites: Topology I (Manifolds).

The course mark will be based on attendence, as well as a problem set that I hope to have ready around end of October. (I'll try to not make it too difficult.)

Course notes will be posted
here.

Last update: October 1, 2017

Our main references are:

- Moerdijk-Mcrun:
** Introduction to Foliations and Lie Groupoids. ** Cambridge University Press
- Crainic-Fernandes:
** Lectures on Integrability of Lie Brackets. **
Available at
this link.
- Cannas da Silva-Weinstein:
** Geometric models for noncommutative algebras,** Berkeley Math. Lecture Notes 10, Amer. Math. Soc. (1999).

Additional references:
- K. Mackenzie:
** General theory of Lie groupoids and Lie algebroids **
- E. Meinrenken:
** Poisson Geometry from a Dirac perspective.**
Available at the
arXiv.