Seminars

# Atiyah, Todd classes, and deformation quantization of DG manifolds

Author:    Publicsh date:2018-06-04    Clicks:
Title: Atiyah, Todd classes, and deformation quantization of DG manifoldsSpeaker: 向茂松博士（北京大学，北京国际数学研究中心）Time: 2018年6月5日11:00-12:00Location: Center for Mathematical Sciences, Room 813Abstract: The notion of DG (differential graded) manifold, also known as NQ supermanifold, is a generalization of the notion of smooth manifolds from ordinary geometry to higher geometry, sp...

Title: Atiyah, Todd classes, and deformation quantization of DG manifolds

Speaker: 向茂松博士（北京大学，北京国际数学研究中心）

Time: 2018年6月5日11:00-12:00

Location: Center for Mathematical Sciences, Room 813

Abstract:

The notion of DG (differential graded) manifold, also known as NQ supermanifold, is a generalization of the notion of smooth manifolds from ordinary geometry to higher geometry, specifically to DG geometry. In this talk, we first review Atiyah and Todd classes of complex manifolds, and how they are intertwined with Kontsevich's formality theorem. Then we recall their generalizations to Lie algebroid pairs and DG manifolds, respectively. We study, in particular, Atiyah and Todd classes of the DG manifold $(F[1],d_F)$ coming from an integrable distribution $F \subset T_{\mathbb{K}} M = TM \otimes_{\mathbb{R}} \mathbb{K}$, where $\mathbb{K} = \mathbb{R}$ or $\mathbb{C}$. It develops a framework that encompasses both the original Atiyah class of holomorphic vector bundles and Molino class of real vector bundles foliated over a foliation as special cases. This is a joint work with Zhuo Chen and Ping Xu.