Configuration complexes and a variant of Cathelineau's complex in weight 3

Abstract

In this paper we consider the Grassmannian complex of projective configurations in weight 2 and 3, and Cathelineau's infinitesimal polylogarithmic complexes. Our main result is a morphism of complexes between the Grassmannian complex and the associated infinitesimal polylogarithmic complex. In order to establish this connection we introduce an $F$-vector space ${\beta }_2^D(F)$, which is an intermediate structure between a $\varmathbb{Z}$-module ${\mathcal{B}}_2(F)$ (scissors congruence group for $F$) and Cathelineau's $F$-vector space ${\beta }_2(F)$ which is an infinitesimal version of it. The structure of ${\beta }_2^D(F)$ is also infinitesimal but it has the advantage of satisfying similar functional equations as the group ${\mathcal{B}}_2(F)$. We put this in a complex to form a variant of Cathelineau's infinitesimal complex for weight 2.

References in corpus (1)

• An extended version of additive K-theory

Cited by in corpus (2)

• Tangent to Bloch-Suslin and Grassmannian Complexes over the dual numbers
• Morphisms Between Classical and Infinitesimal Polylogarithmic and Grassmannian Complexes