Geodesic
K-theory and the enriched Tits building
Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 459-513.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 19D06, 55R35, 55N15
Keywords: Borel construction, flag complex, K-theory, Bloch group, homotopy types, enriched Tits building 
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Nori, M.V.; Srinivas, V. K-theory and the enriched Tits building. Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 459-513. http://geodesic.mathdoc.fr/item/DOCMA_2010__S4__a7/