06219nas a2200145 4500008004100000022001300041245011100054210006900165260001500234300001400249490000700263520571500270100001705985856007106002 2005 eng d a0040938300aExponential iterated integrals and the relative solvable completion of the fundamental group of a manifold0 aExponential iterated integrals and the relative solvable complet c2005/03/01 a351 - 3730 v443 a

We develop a class of integrals on a manifold M called exponential iterated integrals  , an extension of K.T. Chen's iterated integrals. It is shown that the matrix entries of any upper triangular representation of π1(M,x) can be expressed via these new integrals. The ring of exponential iterated integrals contains the coordinate rings for a class of universal representations, called the relative solvable completions   of π1(M,x). We consider exponential iterated integrals in the particular case of fibered knot complements, where the fundamental group always has a faithful relative solvable completion.

1 aMiller, Carl uhttp://www.sciencedirect.com/science/article/pii/S0040938304000795