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

Kasprowski, Daniel

doi:10.2140/agt.2015.15.3467

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

Daniel Kasprowski

Algebraic & Geometric Topology 15 (2015) 3467–3483

DOI: 10.2140/agt.2015.15.3467

Abstract

We prove that for every finitely generated subgroup $G$ of a virtually connected Lie group which admits a finite-dimensional model for $\underline{E} G$ , 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/

Volume 15, issue 6 (2015)