Séminaire Physique mathématique ICJ

Deformations and normal forms of dg-manifolds and their applications

par Arkady Vaintrob (University of Oregon)

Europe/Paris
112 (Institut Camille Jordan)

112

Institut Camille Jordan

Université Lyon 1, Bât. Braconnier, 21 av. Claude Bernard, 69100 Villeurbanne
Description
A differential-graded (dg) manifold is a manifold with a sheaf of commutative dg-algebras. (They are also known as Q-manifolds or supermanifolds with homological vector fields.) I will first discuss general results about deformations and local normal forms of dg-manifolds and related structures (such as dg-submanifolds and bundles). Then I will show how they can be used in the study of more "traditional" structures, such as Poisson manifolds, Lie algebroids, Lie bialgebroids, homotopy actions, generalized complex manifolds, etc.