Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4582497 | Expositiones Mathematicae | 2009 | 11 Pages |
Abstract
In this note we define the Chern–Simons classes of a flat superconnection, D+LD+L, on a complex Z/2ZZ/2Z-graded vector bundle EE on a manifold such that DD preserves the grading and LL is an odd endomorphism of EE. 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>1.
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Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Jaya N.N. Iyer, Uma N. Iyer,