Related papers: Coefficients for the Farrell-Jones Conjecture
We study the Farrell-Jones Conjecture with coefficients in an additive G-category with involution. This is a variant of the L-theoretic Farrell-Jones Conjecture which originally deals with group rings with the standard involution. We show…
We prove that the Farrell-Jones isomorphism conjecture for non-connective algebraic K-theory for a discrete group G and a coefficient ring R holds true if G belongs to the class of groups acting on trees, under certain conditions on G (see…
We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for GL_n(Z).
This is a survey on the Farrell-Jones Conjecture about the algebraic K- and L-theory of groups rings and its applications to algebra, geometry, group theory, and topology.
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…
We prove the Farrell-Jones Isomorphism Conjecture about the algebraic K-theory of a group ring RG in the case where the group G is the fundamental group of a closed Riemannian manifold with strictly negative sectional curvature. The…
Let G be a cocompact lattice in a virtually connected Lie group or the fundamental group of a 3-manifold. We prove the K-theoretic Farrell-Jones Conjecture (up to dimension one) and the L-theoretic Farrell-Jones Conjecture for G, where we…
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…
We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for virtually solvable groups.
We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.
We prove the K- and the $L$-theoretic Farrell-Jones conjecture with coefficients in additive categories and with finite wreath products for arbitrary lattices in virtually connected Lie groups.
In this paper, we prove the K-theoretical and L-theoretical Farrell-Jones Conjecture with coefficients in an additive category for nearly crystallographic groups of the form $\mathbb{Q}^n \rtimes \mathbb{Z}$, where $\mathbb{Z}$ acts on…
We prove the K-theoretic Farrell-Jones conjecture with (twisted) coefficients for CAT(0)-groups.
We use the controlled algebra approach to study the problem that whether the Farrell-Jones conjecture is closed under passage to over-groups of finite indices. Our study shows that this problem is closely related to a general problem in…
In this note, we prove the K- and L-theoretic Farrell-Jones Conjecture with coefficients in an additive category for fundamental groups of graphs of virtually cyclic groups.
This article will explore the K- and L-theory of group rings and their applications to algebra, geometry and topology. The Farrell-Jones Conjecture characterizes K- and L-theory groups. It has many implications, including the Borel and…
We give a survey of the meaning, status and applications of the Baum-Connes Conjecture about the topological K-theory of the reduced group C^*-algebra and the Farrell-Jones Conjecture about the algebraic K- and L-theory of the group ring of…
We prove the $K$- and $L$-theoretic Farrell-Jones Conjecture with coefficients in an additive category for every normally poly-free group, in particular for even Artin groups of FC-type, and for all groups of the form $A\rtimes \mathbb{Z}$…
In this paper, we prove the Farrell-Jones Conjecture for the solvable Baumslag-Solitar groups with coefficients in an additive category. We also extend our results to groups of the form, Z[1/p] semidirect product with any virtually cyclic…
We show that the class of groups satisfying the K- and L-theoretic Farrell-Jones conjecture is closed under taking graph products of groups.