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.
Classical polylogarithms, Grassmannian, chain complexes, generalization
KHALID, MUHAMMAD; KHAN, JAVED; and IQBAL, AZHAR
"Generalized geometry of Goncharov and configuration complexes,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 60.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/60