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Generalized geometry of Goncharov and configuration complexes. (English) Zbl 1424.11099

Summary: 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.

MSC:

11G55 Polylogarithms and relations with \(K\)-theory
14M15 Grassmannians, Schubert varieties, flag manifolds
18G35 Chain complexes (category-theoretic aspects), dg categories
55T25 Generalized cohomology and spectral sequences in algebraic topology
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