Mathematics – Geometric Topology
Scientific paper
2002-02-23
Topology 44 (2005) 351-373
Mathematics
Geometric Topology
30 pages. New version is revised throughout, and includes a stronger result in section 7 and more extensive discussion of exam
Scientific paper
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 the fundamental group of M can be expressed via these new integrals. The ring of exponential iterated integrals contains the coordinate rings for a class of universal representations, called relative solvable completions, of the fundamental group. We consider exponential iterated integrals in the particular case of fibered knot complements, where the fundamental group always has a faithful relative solvable completion.
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