Deformation theory & Lie groupoids seminar
Deformation theory & Lie groupoids seminar
Embedded Files
General information
General information
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.
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, Déformations 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.
Talk 3 (March 20): The deformation cohomology of a Lie algebroid. Computation of H^0, H^1 and H^2. Relationship of H^2 and the classification of the deformations of a Lie algebroid. Examples: Lie algebras, deformation rigidity of the tangent bundle, relations with foliated cohomology. The long exact sequence of the deformation cohomology of a regular Lie algebroid.
Talks on Déformations des feuilletages
Talk 4 (March 27): Foliations via cocycles. S-deformation of a foliation and its germ. The monodromy groupoid of a foliation with respect to a complete transversal, and the associated holonomy functor. The S-deformation of the holonomy functor and generalized maps of Lie groupoids. Statement of the Bonatti-Haefliger theorem on deformations of foliations.
Talk 5 (April 3): Sketch of the proof of the Bonatti-Haefliger theorem.
Page updated
Google Sites
Report abuse