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BIMSA 代数几何讨论班
BIMSA 代数几何讨论班
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
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.