报告题目： Ideal systems and characteristic classes

报 告 人：Madeleine Jotz Lean 教授 德国哥廷根大学

报告时间：2021年1月7日 16:00-17:00

报告地点：Join Zoom Meeting
https://uni-goettingen.zoom.us/j/97020051076?pwd=RitLdUQ5blZFSjZvSm94Z3ExTnI2QT09
Meeting ID: 970 2005 1076         Passcode: 658281

校内联系人：生云鹤 shengyh@jlu.edu.cn

报告摘要：

This talk describes the Atiyah class of a Lie pair (due to Laurent-Gengoux, Stiénon and Xu) and defines analogously the Atiyah class of an infinitesimal ideal system. The latter objects are considered the right notion of ideal in the context of Lie algebroids. The Atiyah class of a Lie pair turns then out to be an obstruction to the existence of an ideal system (à la Mackenzie and Higgins) on the Lie pair. Then we will discuss representations up to homotopy of Lie algebroids on graded vector bundles, in particular the adjoint representation up to homotopy of a Lie algebroid.  The graded trace of the powers of the curvature of a connection up to homotopy induces characteristic classes of graded vector bundles.  This yields obstructions to the existence of a representation up to homotopy on a graded vector bundle. As an immediate consequence, we find an obstruction to an infinitesimal ideal system in a Lie algebroid A over M, in terms of the Pontryagin classes of the underlying vector subbundles of TM and of A.

报告人简介：

Madeleine Jotz Lean，德国哥廷根大学教授，从事微分几何的研究，在Math. Ann.、Tran. AMS、IMRN、J. Math. Pures Appl.以及 J. Symplectic Geom.等杂志发表多篇文章，在国际上有重要的影响力。