Chern-simons Classes for a Superconnection
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چکیده
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.
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تاریخ انتشار 2009