[geometry-ml:06843] 数理解析研究所セミナーのお知らせ(6/1)

[Noriaki Ikeda]

各位

下記の通り，6月1日（月）10:30から京都大学数研セミナーが以下のようにおこなわれますのでお知らせいたします。

日時: 6月1日（月） 10:30～11:30
会場: 京都大学数理解析研究所206号室

Speaker: Mathieu Stiénon (Pennsylvania State University)

Title: Atiyah class and formal exponential maps of differential graded 
manifolds

Abstract: Exponential maps arise naturally in the contexts of Lie theory 
and smooth manifolds. The infinite jets of these classical exponential 
maps are related to Poincaré–Birkhoff–Witt isomorphisms and the complete 
symbols of differential operators. It turns out that these formal 
exponential maps can be extended to the context of graded manifolds.

For dg manifolds, the formal exponential maps need not be compatible 
with the homological vector field and the incompatibility is captured by 
a cohomology class reminiscent of the Atiyah class of holomorphic vector 
bundles.

Indeed, the space of vector fields on a dg manifold carries a natural 
$L_\infty$ algebra structure whose binary bracket is a cocycle 
representative of the Atiyah class of the dg manifold. This $L_\infty$ 
algebra is essentially a generalization of the one on the Dolbeault 
complex of a Kähler manifold discovered by Kapranov in his work on 
Rozansky-Witten invariants.

https://www.kurims.kyoto-u.ac.jp/ja/seminar/seminar-ikeda.html

池田憲明
京都大学数理解析研究所、立命館大学