Iterated integrals of superconnections

Understand

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.