On the Farrell-Jones Conjecture and its applications

Abstract

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 study inheritance properties. We discuss new applications, focussing on the Bass Conjecture, the Kaplansky Conjecture and conjectures generalizing Moody's Induction Theorem. Thus we extend the class of groups for which these conjectures are known considerably.

References in corpus (2)

• Inheritance of Isomorphism Conjectures under colimits
• Induction Theorems and Isomorphism Conjectures for K- and L-Theory

Cited by in corpus (2)

• Inheritance of Isomorphism Conjectures under colimits
• The Borel conjecture for manifolds with virtually solvable fundamental groups