Generalized geometry of Goncharov and configuration complexes

Authors: MUHAMMAD KHALID, JAVED KHAN, AZHAR IQBAL

Abstract: In this article, a generalized geometry of Goncharov's complex and the Grassmannian complex will be proposed. First, all new homomorphisms will be defined, and then they will be used extensively to connect the Bloch--Suslin and the Grassmannian complex for weight $n=2$ and then Goncharov's complex with Grassmannian complex for weight $n=3$, up to $n=6$. Lastly, and most importantly, generalized morphisms will be presented to cover the geometry of the Goncharov and Grassmannian complex when weight $n= N$. Associated diagrams will be exhibited, proven to be commutative.

Keywords: Classical polylogarithms, Grassmannian, chain complexes, generalization

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