Algebraic hulls of solvable groups and exponential iterated integrals on solvmanifolds

TL;DR

This paper explores the algebraic structures of solvable groups and solvmanifolds using exponential iterated integrals, extending classical concepts to a broader class of groups.

Contribution

It introduces a novel representation of algebraic hulls of solvable groups via exponential iterated integrals, generalizing Malcev completions.

Findings

Representation of algebraic hulls using exponential iterated integrals

Extension of Chen's iterated integrals to solvable groups

Connection between algebraic hulls and differential forms on solvmanifolds

Abstract

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