On the homological interpretation of the prounipotent completion of the fundamental group

TL;DR

This paper explores the cohomological perspective of unipotent quotients of the fundamental groupoid of algebraic complex varieties and introduces a homological construction of transition morphisms.

Contribution

It provides a new homological construction of transition morphisms for unipotent quotients of fundamental groupoids, extending previous cohomological interpretations.

Findings

Cohomological interpretation of unipotent quotients clarified

Homological construction of transition morphisms developed

Links between fundamental groupoids and singular homology established

Abstract

We recall the cohomological interpretation of the unipotent quotients of the fundamental groupoid of an algebraic complex variety (Beilinson, Deligne-Goncharov). We then give a construction of the resutting transition morphisms in terms of singular homology.