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BIMSA AG Seminar
Differential graded manifolds, homological vector fields, and deformations of geometric structures
Differential graded manifolds, homological vector fields, and deformations of geometric structures
演讲者
Arkady Vaintrob
时间
2025年05月20日 15:00 至 16:00
地点
A7-201
线上
Zoom 638 227 8222
(BIMSA)
摘要
A differential-graded (dg) manifold is a manifold equipped with a sheaf of quasi-free differential graded algebras. Equivalently, it can be described as a supermanifold with a homological vector field, an odd self-commuting vector field. Many geometric and algebraic structures can be naturally characterized in terms of homological vector fields.
I will begin by presenting general results on deformations and normal forms of homological vector fields and related structures, such as dg-submanifolds and dg-bundles. I will then show how they can be used in the study of classical geometric structures, such as Poisson manifolds, Lie (bi)algebroids, (generalized) complex structures, homotopy actions, etc.
I will begin by presenting general results on deformations and normal forms of homological vector fields and related structures, such as dg-submanifolds and dg-bundles. I will then show how they can be used in the study of classical geometric structures, such as Poisson manifolds, Lie (bi)algebroids, (generalized) complex structures, homotopy actions, etc.