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

2012/05/17 by Raziuddin Siddiqui, Siddiqui, Raziuddin
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1205.3864

arxiv created 2012/06/08 · arxiv updated 2012/06/11

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 β^D₂(F), which is an intermediate structure between a \varmathbbZ-module B₂(F) (scissors congruence group for F) and Cathelineau's F-vector space β₂(F) which is an infinitesimal version of it. The structure of β^D₂(F) is also infinitesimal but it has the advantage of satisfying similar functional equations as the group B₂(F). We put this in a complex to form a variant of Cathelineau's infinitesimal complex for weight 2.

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