Abstract: This talk is based on the authors paper of the same title. It discusses various geometric constructions associated with fibre bundles, which share one common trait: they all are phrased in the terms of an important algebraic object, the twisting cochain. Examples include the Chern-Weil classes, holonomy representation and the so-called cyclic Chern character of Bismut and others, also called the Bismut’s class. We also give several examples of twisting cochains associated with a given principal bundle. In particular, our approach allows us to obtain explicit formulas for the Chern classes and for an analogue of the cyclic Chern character in the terms of the glueing functions of the principal bundle and discuss few modifications of this construction. We hope that this approach can turn fruitful for the study of various applications of the characteristic classes, e.g. of the index formula.
Speaker: G. Sharygin (MSU, SRMC)
Time: 16:00~19:00, Friday, December 20, 2024
Location: Room 1410, SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai
English 
简体中文