Related papers: The Farrell-Jones Conjecture for cocompact lattice…
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.
We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for virtually solvable groups.
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.
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.
We introduce the Farrell-Jones Conjecture with coefficients in an additive category with G-action. This is a variant of the Farrell-Jones Conjecture about the algebraic K- or L-Theory of a group ring RG. It allows to treat twisted group…
We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for GL_n(Z).
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…
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 show that the class of groups satisfying the K- and L-theoretic Farrell-Jones conjecture is closed under taking graph products of 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 Farrell-Jones Conjecture for (non-connective) $A$-theory with coefficients and finite wreath products for hyperbolic groups, CAT(0)-groups, cocompact lattices in almost connected Lie groups and fundamental groups of manifolds…
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-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.
The Farrell-Jones Fibered Isomorphism Conjecture for the stable topological pseudoisotopy theory has been proved for several classes of groups. For example for discrete subgroups of Lie groups, virtually poly-infinite cyclic groups, Artin…
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 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 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…
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.
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 prove the K-theoretic Farrell-Jones conjecture with (twisted) coefficients for CAT(0)-groups.