Algebraic hulls of solvable groups and exponential iterated integrals on solvmanifolds

We represent the coordinate ring of algebraic hulls (which are the fundamental groups of generalizations of the Malcev completions of nilpotent groups for solvable groups) of solvmanifolds G/Γ by using Miller’s exponential iterated integrals (which are extensions of Chen’s iterated integrals) of invariant differential forms.