Lectures on integrability of Lie brackets by Crainic and Fernandes- notes available through the link, expanded version available upon request.
Aim: to give a short introduction into the geometry of Lie algebroids/Lie groupoids and to understand some of the recent work on the relationship with the classification of G-structures. Again, we plan to start with some rather introductory courses, spending some time with the standard setting of Lie groups and Lie group actions.
Literature: For an introduction to Lie groupoids and Lie algebroids, we will use:
Lectures on integrability of Lie brackets by Crainic and Fernandes- notes available through the link, expanded version available upon request.
For the same subject one can also use the books mentioned above: the one by Dufour-Zung or Moerdijk-Mrcun, or
Geometric models for noncommutative algebras by Cannas da Silva and Weinstein.
For G-structures we will use:
Transformation groups in differential geometry by Kobayashi.
The infinite groups of Lie and Cartan. I. The transitive groups. by Guillemin and Sternberg.
Finally, for the recent results on Lie algebroids and the classification of geometric structures, we will use:
The classifying Lie algebroid of a geometric structure- PhD thesis of Ivan Struchiner (not available yet- instead, one can have a look at this preprint by Struchiner and Fernandes).
Level: Beginning PhD students and Master students interested in Differential Geometry.
Person in charge: Maria Amelia Salazar and Camilo Arias Abad.