Iterated integrals of superconnections

Abstract

Starting with a Z-graded superconnection on a graded vector bundle over a smooth manifold M, we show how Chen's iterated integration of such a superconnection over smooth simplices in M gives an A-infinity functor if and only if the superconnection is flat. If the graded bundle is trivial, this gives a twisting cochain. Very similar results were obtained by K.T. Chen using similar methods. This paper is intended to explain this from scratch beginning with the definition and basic properties of a connection and ending with an exposition of Chen's "formal connections" and a brief discussion of how this is related to higher Reidemeister torsion.

40 pages, 3 figures

References in corpus (1)

• Morse theory and higher torsion invariants II

Cited by in corpus (9)

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• Singular chains on Lie groups and the Cartan relations II
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