Volume 15, issue 3 (2015)

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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
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