Related papers: The Farrell-Jones conjecture for arbitrary lattice…

We prove the A-theoretic Isomorphism Conjecture with coefficients and finite wreath products for solvable groups.

This note surveys axiomatic results for the Farrell-Jones Conjecture in terms of actions on Euclidean retracts and applications of these to GL_n(Z), relative hyperbolic groups and mapping class groups.

We prove that the Fibered Isomorphism Conjecture of T. Farrell and L. Jones holds for various mapping class groups. In many cases, we explicitly calculate the lower algebraic K-groups, showing that they do not always vanish.

We prove the Farrell-Jones fibered isomorphism conjecture for several classes of Artin groups of finite and affine types. As a consequence, we compute explicitly the surgery obstruction groups of the finite type pure Artin groups.

We prove the Farrell-Jones Conjecture for mapping tori of automorphisms of virtually torsion-free hyperbolic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture by…

For a group G relatively hyperbolic to a family of residually finite groups satisfying the Farrell-Jones conjecture, we reduce the solution of the Farrell-Jones conjecture for G to the case of certain nice cyclic extensions in G.

We prove that the Waldhausen nilpotent class group of an injective index 2 amalgamated free product is isomorphic to the Farrell-Bass nilpotent class group of a twisted polynomial extension. As an application, we show that the Farrell-Jones…

We prove the Baum--Connes conjecture with arbitrary coefficients for some classes of groups: (1) Linear algebraic groups over a non-archimedean local field. (2) Linear algebraic groups over the adeles of a global field k, provided that at…

This is the first of three articles on the Fibered Isomorphism Conjecture of Farrell and Jones for L-theory. We apply the general techniques developed in [15] and [16] to the L-theory case of the conjecture and prove several results. Here…

We construct a Dirac morphism and prove that if this Dirac morphism is invertible, then the isomorphism conjecture for non-connective algebraic K-theory holds true.

Motivated by the Farrell-Jones Conjecture for group rings, we formulate the $\mathcal{C}$op-Farrell-Jones Conjecture for the K-theory of Hecke algebras of td-groups. We prove this conjecture for (closed subgroups of) reductive p-adic groups…

We show that for groups acting acylindrically on simplicial trees the $K$- and $L$-theoretic Farrell-Jones Conjecture relative to the family of subgroups consisting of virtually cyclic subgroups and all subconjugates of vertex stabilisers…

Let G be a group and k a field of characteristic zero. We prove that if the Farrell-Jones conjecture for the K-theory of R[G] is satisfied for every smooth k-algebra R, then it is also satisfied for every commutative k-algebra R.

We prove that for every finitely generated subgroup of a virtually connected Lie group which admits a finite dimensional model for the classifying space for proper actions the assembly map in algebraic K-theory is split injective. We also…

We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite simple groups, and for large subsets of groups of…

In this article we study a coarse version of the K-theoretic Farrell-Jones conjecture we call coarse or bounded isomorphism conjecture. With techniques that have already been used to prove the Farrell-Jones conjecture for hyperbolic groups…

In this paper, we prove the K- and L-theoretical Isomorphism Conjecture for Baumslag-Solitar groups with coefficients in an additive category.

We generalize the proof of the Farrell-Jones conjecture for CAT(0)-groups to a larger class of groups in particular also containing all hyperbolic groups. This way we give a unified proof for both classes of groups.

We show that the subgroup lattice of any finite group satisfies Frankl's Union-Closed Conjecture. We show the same for all lattices with a modular coatom, a family which includes all supersolvable and dually semimodular lattices. A common…

We observe an inductive structure in a large class of Artin groups and exploit this information to deduce the Farrell-Jones isomorphism conjecture for several classes of Artin groups of finite real, complex and affine types.