Morphisms Between Classical and Infinitesimal Polylogarithmic and Grassmannian Complexes

TL;DR

This paper constructs commutative diagrams linking various complexes in algebraic K-theory and polylogarithms, revealing their interrelations for weights 2 and 3 to unify different approaches.

Contribution

It introduces two comprehensive diagrams connecting Grassmannian, Bloch-Suslin, Goncharov, and Cathelineau complexes, providing a unified geometric and algebraic framework.

Findings

Unified view of complexes for weights 2 and 3

Clarified relations between geometric and algebraic complexes

Enhanced understanding of polylogarithmic and K-theoretic structures

Abstract

In this paper we want to introduce two commutative diagrams for weight $n$=2 and $n$=3 with six faces on each. These diagrams describe the relations between Grassmannian complex in geometric configurations, Bloch-Suslin's complex for weight $n$=2 and Goncharov's complex for weight $n$=3 and the variants of Cathelineau's complexes for weight $n$=2,3. Here we are putting all complexes together to see a bigger picture.