Generalized geometry of Goncharov and configuration complexes

Authors : Muhammad KHALID, Javed KHAN, Azhar IQBAL

Pages : 1509-1527

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Publication Date : 0000-00-00

Article Type : Research Paper

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