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Daniel Kasprowski (MPI): On the K-theory of groups with finite decomposition complexity (02/12/2014)


Decomposition complexity is a generalization of asymptotic dimension. For example all linear groups have finite decomposition complexity. By a result of Ramras, Tessera and Yu the $K$-theoretic assembly map

H_n^G (BG;\bbK_R) \to K_n(R[G])

is split injective for every group $G$ with finite decomposition complexity that admits a finite model for $BG$ (and therefore is torsion-free). We give a generalization of this result which in particular implies that for a finitely generated subgroup $G$ of a virtually connected Lie group with a finite dimensional model for $\underbar EG$ the above assembly map is split injective.

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