K-Theory and the Enriched Tits Building

Motivated by the splitting principle, we define certain simplicial complexes associated to an associative ring $A$, which have an action of the general linear group $GL(A)$. This leads to an exact sequence, involving Quillen's algebraic K-groups of $A$ and the symbol map. Computations in low degrees lead to another view on Suslin's theorem on the Bloch group, and perhaps show a way towards possible generalizations.

2010 Mathematics Subject Classification: 19D06,~51A05,~55P10

Keywords and Phrases: $K_i(A)$, geometries, homotopy types

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