Geometry of configurations in tangent groups

Abstract

This article relates the Grassmannian complexes of geometric configurations to the tangent to the Bloch-Suslin complex and to the tangent to Goncharov’s motivic complex. By means of morphisms, we bring the geometry of configurations in tangent groups, $T\mathcal{B}_2(F)$ and $T\mathcal{B}_3(F)$ that produce commutative diagrams. To show the commutativity of diagrams, we use combinatorial techniques that include permutations in symmetric group S6. We also create analogues of the Siegel’s cross-ratio identity for the truncated polynomial ring F[ε]ν.

Keywords

• affine spaces
• cross-ratio
• tangent complex
• odd permutation
• symmetric group