The Farrell–Jones conjecture for some nearly crystallographic groups

Farrell, F Thomas; Wu, Xiaolei

doi:10.2140/agt.2015.15.1667

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The Farrell–Jones conjecture for some nearly crystallographic groups

F Thomas Farrell and Xiaolei Wu

Algebraic & Geometric Topology 15 (2015) 1667–1690

DOI: 10.2140/agt.2015.15.1667

Abstract

In this paper, we prove the K–theoretical and L–theoretical Farrell–Jones conjecture with coefficients in an additive category for nearly crystallographic groups of the form $ℚ^{n} ⋊ ℤ$ , where $ℤ$ acts on $ℚ^{n}$ as an irreducible integer matrix with determinant $d$ , $| d | > 1$ .

Keywords

tree, group action, Farrell–Jones conjecture, K–theory of group rings, L–theory of group rings

Mathematical Subject Classification 2010

Primary: 18F25

Secondary: 19A31, 19B28

References

Publication

Received: 28 May 2014

Revised: 26 August 2014

Accepted: 2 October 2014

Published: 19 June 2015

Authors

F Thomas Farrell
Department of Mathematical Sciences SUNY Binghamton Binghamton NY 13902-6000 USA

Xiaolei Wu
Institut für Mathematik Freie Universität Berlin Arnimallee 7 D-14195 Berlin Germany

Volume 15, issue 3 (2015)