Related papers: Coefficients for the Farrell-Jones Conjecture

We prove the A-theoretic Farrell-Jones Conjecture for virtually solvable groups. As a corollary, we obtain that the conjecture holds for S-arithmetic groups and lattices in almost connected Lie groups.

In this short note we prove that the Farrell-Jones Fibered Isomorphism Conjecture in L-theory, after inverting 2, is true for a group whose some derived subgroup is free.

We prove the Farrell-Jones conjecture for free-by-cyclic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture.

We study the Fibered Isomorphism Conjecture of Farrell and Jones in L-theory for groups acting on trees. In several cases we prove the conjecture. This includes wreath products of abelian groups and free metabelian groups. We also deduce…

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 discuss an analogon to the Farrell-Jones Conjecture for homotopy algebraic K-theory. In particular, we prove that if a group G acts on a tree and all isotropy groups satisfy this conjecture, then G satisfies this conjecture. This result…

We show how the existing proof of the Farrell-Jones Conjecture for virtually poly-$\mathbb{Z}$-groups can be improved to rely only on the usual inheritance properties in combination with transfer reducibility as a sufficient criterion for…

We investigate when Isomorphism Conjectures, such as the ones due to Baum-Connes, Bost and Farrell-Jones, are stable under colimits of groups over directed sets (with not necessarily injective structure maps). We show in particular that…

We prove the $K$ and $L$ theoretic versions of the Fibered Isomorphism Conjecture of F. T. Farrell and L. E. Jones for braid groups on a surface.

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…

We develop a version of controlled algebra for simplicial rings. This generalizes the methods which lead to successful proofs of the algebraic K- theory isomorphism conjecture (Farrell-Jones Conjecture) for a large class of groups. This is…

A group pair $(G, X)$ consists of a group $G$ together with a $G$-set $X$. Such a pair encodes properties of $G$ relative to the stabilisers of points in $X$. In this paper, we show how to combine properties of group pairs and their…

In this paper, we introduce a notion of twisted Roe algebra and a twisted coarse Baum-Connes conjecture with coefficients. We will study the basic properties of twisted Roe algebras, including a coarse analogue of the imprimitivity theorem…

We show that the Farrell-Jones Conjecture holds for fundamental groups of graphs of groups with abelian vertex groups. As a special case, this shows that the conjecture holds for generalized Baumslag-Solitar groups.

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 call a group FJ if it satisfies the $K$- and $L$-theoretic Farrell-Jones conjecture with coefficients in $\mathbb Z$. We show that if $G$ is FJ, then the simple Borel conjecture (in dimensions $\ge 5$) holds for every group of the form…

We show that contracting self-similar groups satisfy the Farrell-Jones conjectures as soon as their universal contracting cover is non-positively curved. This applies in particular to bounded self-similar groups. We define, along the way, a…

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 fibred Farrell--Jones Conjecture (FJC) in $A$-, $K$-, and $L$-theory for a large class of suspensions of relatively hyperbolic groups, as well as for all suspensions of one-ended hyperbolic groups. We deduce two applications:…

We establish formulas for computation of the higher algebraic $K$-groups of the endomorphism rings of objects linked by a morphism in an additive category. Let ${\mathcal C}$ be an additive category, and let $Y\ra X$ be a covariant morphism…