Generalized geometry of Goncharov and configuration complexes

Authors : Muhammad Khalid, Javed Khan, Azhar Iqbal

Pages : 1509-1527

View : 11 | Download : 6

Publication Date : 9999-12-31

Article Type : Makaleler

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