MAT 1341F Topics in Differential Geometry: Lie Groupoids and Lie Algebroids
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:
Prerequisites: Topology I (Manifolds).
- 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 (?)
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
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.
- Cannas da Silva-Weinstein: Geometric models for noncommutative algebras, Berkeley Math. Lecture Notes 10, Amer. Math. Soc. (1999).
- K. Mackenzie: General theory of Lie groupoids and Lie algebroids
- E. Meinrenken: Poisson Geometry from a Dirac perspective.
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