Infinitesimal and tangent to polylogarithmic complexes for higher weight

Abstract

Motivic and polylogarithmic complexes have deep connections with $K$-theory. This article gives morphisms (different from Goncharov's generalized maps) between $\Bbbk$-vector spaces of Cathelineau's infinitesimal complex for weight $n$. Our morphisms guarantee that the sequence of infinitesimal polylogs is a complex. We are also introducing a variant of Cathelineau's complex with the derivation map for higher weight $n$ and suggesting the definition of tangent group $T\mathcal{B}_n(\Bbbk)$. These tangent groups develop the tangent to Goncharov's complex for weight $n$.

Keywords

• polylogarithm
• infinitesimal complex
• five term relation
• tangent complex