The Farrell–Jones conjecture for some nearly crystallographic groups

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 ${\mathbb{Q}}^n⋊\mathbb{Z}$, where $\mathbb{Z}$ acts on ${\mathbb{Q}}^n$ as an irreducible integer matrix with determinant $d$, $\left|d\right|>1$.