On the Farrell–Jones Conjecture and its applications

By Arthur Bartels, W. Lück, H. Reich. 2007

76 citations recorded by the source corpus.

We present the status of the Farrell–Jones Conjecture for algebraic K‐theory for a group G and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be true, and we study inheritance properties. We discuss new applications, focussing on the Bass Conjecture, the Kaplansky Conjecture, and conjectures generalizing Moody's Induction Theorem. Thus, we considerably extend the class of groups for which these conjectures are known.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/543db927d4ce7eb1969fc47bb394b883fcbf6fda

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The K-theoretic Farrell–Jones conjecture for hyperbolic groups (2007, background): “For explanations, proofs and further applications in a more general context we refer to [6].”
The Farrell–Jones conjecture for arbitrary lattices in virtually connected Lie groups (2014, background): “For an overview of the Farrell-Jones conjecture and its consequences, see for instance [5, 20, 21].”
The Farrell-Jones Conjecture for cocompact lattices in virtually connected Lie groups (2011, background): “For a detailed discussion of these applications we refer to [10] and the survey article [30].”
The Borel Conjecture for hyperbolic and CAT(0)-groups (2009, methodology): “These and further applications of the Farrell-Jones Conjectures are discussed in detail in [9] and [42].”