Ecalle's dimorphic transportation and Brown's lifting

TL;DR

This paper connects Brown's lifting procedure for solving double shuffle equations with Ecalle's dimorphic transportation framework, providing a new perspective on the underlying mathematical structure.

Contribution

It demonstrates that Brown's lifting can be understood within Ecalle's dimorphic transportation framework, offering a novel conceptual link.

Findings

Brown's lifting is described by Ecalle's framework

Double shuffle equations relate to linearized solutions

New perspective on solving algebraic equations

Abstract

Brown's lifting procedure shows that one can solve the double shuffle equations modulo products from solutions of linearized ones. In this paper, we reveal that it is described in the framework of Ecalle's dimorphic transportation.