Volume 15, issue 6 (2015)

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On the $K$–theory of subgroups of virtually connected Lie groups

Daniel Kasprowski

Algebraic & Geometric Topology 15 (2015) 3467–3483
Abstract

We prove that for every finitely generated subgroup $G$ of a virtually connected Lie group which admits a finite-dimensional model for $\underset{¯}{E}G$, the assembly map in algebraic $K$–theory is split injective. We also prove a similar statement for algebraic $L$–theory which, in particular, implies the generalized integral Novikov conjecture for such groups.

Keywords
$K$– and $L$–theory of group rings, injectivity of the assembly map, virtually connected Lie groups
Mathematical Subject Classification 2010
Primary: 18F25, 19A31, 19B28, 19G24