  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.
