Algebraic & Geometric Topology

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

Daniel Kasprowski

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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.

Article information

Source
Algebr. Geom. Topol., Volume 15, Number 6 (2015), 3467-3483.

Dates
Received: 24 September 2014
Revised: 9 February 2015
Accepted: 9 April 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841074

Digital Object Identifier
doi:10.2140/agt.2015.15.3467

Mathematical Reviews number (MathSciNet)
MR3450768

Zentralblatt MATH identifier
1345.18016

Subjects
Primary: 18F25: Algebraic $K$-theory and L-theory [See also 11Exx, 11R70, 11S70, 12- XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67] 19A31: $K_0$ of group rings and orders 19B28: $K_1$of group rings and orders [See also 57Q10] 19G24: $L$-theory of group rings [See also 11E81]

Keywords
$K$– and $L$–theory of group rings injectivity of the assembly map virtually connected Lie groups

Citation

Kasprowski, Daniel. On the $K$–theory of subgroups of virtually connected Lie groups. Algebr. Geom. Topol. 15 (2015), no. 6, 3467--3483. doi:10.2140/agt.2015.15.3467. https://projecteuclid.org/euclid.agt/1510841074


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