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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 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
References
Publication
Received: 24 September 2014
Revised: 9 February 2015
Accepted: 9 April 2015
Published: 12 January 2016
Authors
Daniel Kasprowski
Max-Planck-Institut für Mathematik
Vivatsgasse 7
D-53111 Bonn
Germany
http://guests.mpim-bonn.mpg.de/kasprowski/