Chern-Simons classes of flat connections on supermanifolds

2007/07/16 by Iyer, JN, Iyer, Un
#53C05 #53C07 #53C29 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.0707.2321

Abstract

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 Kähler manifold or a smooth complex quasi--projective variety, in degrees > 1.

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