On the Farrell-Jones conjecture for localising invariants

Abstract

We show the Farrell-Jones conjecture with coefficients in left-exact $\infty$-categories for finitely $\mathcal{F}$-amenable groups and, more generally, Dress-Farrell-Hsiang-Jones groups. Our result subsumes and unifies arguments for the K-theory of additive categories and spherical group rings and extends it for example to categories of perfect modules over ${\mathbb{E}}_1$-ring spectra.

arXiv comment133 pages; minor changes following a referee report

References in corpus (8)

• Higher Topos Theory
• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Geodesic flow for CAT(0)-groups
• Equivariant coarse homotopy theory and coarse algebraic $\mathbf{K}$-homology
• Shifted Coisotropic Correspondences
• Algebraic K-theory of group rings and the cyclotomic trace map
• Homotopy theory with marked additive categories
• K-theory and actions on Euclidean retracts