This is the official website for the deformation theory and Lie groupoids seminar, starting on March 6.
Place: MATH731.
Time: every Friday 2PM-3PM.
Prerequisites: the basics of Lie groupoids and Lie algebroids will be reviewed, as well as of foliation theory. Some familiarity with differential geometry/topology is useful.
If you have any questions about the seminar or want to give one of the talks, please send me an email (barata@purdue.edu).
Brief description
The main objective of this reading seminar is to understand the following three articles:
Crainic-Moerdijk, Deformations of the Lie bracket: cohomological aspects.
Bonatti-Haefliger, DĂ©formations des feuilletages.
Crainic-Loja Fernandes, Stability of symplectic leaves.
These are concerned with the study of deformation problems, using the language of Lie groupoids and Lie algebroids. As foliations on a smooth manifold can be understood from this prespective, this language allows us to study the more geometrical problem of deformations of foliations. We hope to also understand this better in this seminar.
See this for more details on the papers above.
Schedule
Talks on Deformations of the Lie bracket: cohomological aspects
Talk 1 (March 6): Notion of Lie groupoid and Lie algebroid. Examples: tangent bundle, Lie algebras, foliations, smooth actions. Introduction to classic deformation theory. Notes.
Talk 2 (March 12): The deformation complex of a Lie algebroid. Definition via multiderivations of Lie algebroids, as done by Crainic-Moerdijk. Definition via representations up to homotopy and the adjoint representation of a Lie algebroid, as done by Abad-Crainic.