Chern-Simons classes of flat connections on supermanifolds

Details Chern-Simons classes of flat connections on supermanifolds Chern-Simons classes of flat connections on supermanifolds

2007-07-16

arxiv.org/abs/0707.2321v1

Mathematics

Algebraic Geometry

Scientific paper

In this note we define Chern-Simons classes of a superconnection $D+L$ on a complex supervector bundle $E$ such that $D$ is flat and preserves the grading, and $L$ is an odd endomorphism of $E$ on a supermanifold. 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. We extend Reznikov's theorem on triviality of these classes when the manifold is a compact K\"ahler manifold or a smooth complex quasi--projective variety, in degrees > 1.

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