Chern–Simons classes for a superconnection

Iyer, Jaya N. N. ; Iyer, Uma N. (2009) Chern–Simons classes for a superconnection Expositiones Mathematicae, 27 (4). pp. 351-361. ISSN 0723-0869


Official URL:

Related URL:


In this note we define the Chern–Simons classes of a flat superconnection, D+L, on a complex Z/2Z-graded vector bundle E on a manifold such that D preserves the grading and L is an odd endomorphism of E. As an application, we obtain a definition of Chern–Simons classes of a (not necessarily flat) morphism between flat vector bundles on a smooth manifold. An application of Reznikov's theorem shows the triviality of these classes when the manifold is a compact Kähler manifold or a smooth complex quasi-projective variety in degrees >1.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Supermanifolds; Connections; Secondary Classes
ID Code:102299
Deposited On:01 Feb 2018 11:03
Last Modified:01 Feb 2018 11:03

Repository Staff Only: item control page