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

Kasprowski, Daniel¹

¹Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany

Algebraic and Geometric Topology, Tome 15 (2015) no. 6, pp. 3467-3483

Résumé

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.

Détail

DOI : 10.2140/agt.2015.15.3467

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

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