Related papers: Relating the Farrell Nil-groups to the Waldhausen …

We prove the K-theoretic Farrell-Jones conjecture with (twisted) coefficients for CAT(0)-groups.

The cyclic sieving phenomenon is a well-studied occurrence in combinatorics appearing when a cyclic group acts on a finite set. In this paper, we demonstrate a natural extension of this theory to finite abelian groups. We also present a…

We prove the Farrell-Jones Conjecture for algebraic K-theory of spaces for virtually poly-Z-groups. For this, we transfer the 'Farrell-Hsiang method' from the linear case to categories of equivariant, controlled retractive spaces.

We study the behavior of the Nil-subgroups of K-groups under localization. As a consequence we obtain that the relative assembly map from the family of finite subgroups to the family of virtually cyclic subgroups is rationally an…

A classical discovery known as Fenchel's conjecture and proved in the 1950s, shows that every co-compact Fuchsian group $F$ has a normal subgroup of finite index isomorphic to the fundamental group of a compact unbordered orientable…

In this paper we generalize the notion of strongly poly-free group to a larger class of groups, we call them strongly poly-surface groups and prove that the Fibered Isomorphism Conjecture of Farrell and Jones corresponding to the stable…

We study connections between self-inversive and self-reciprocal polynomials, reduction theory of binary forms, minimal models of curves, and formally self-dual codes. We prove that if $\mathcal X$ is a superelliptic curve defined over…

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 that the Farrell-Jones assembly map for connective algebraic K-theory is rationally injective, under mild homological finiteness conditions on the group and assuming that a weak version of the Leopoldt-Schneider conjecture holds…

Suppose that a finite group $G$ admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixed point subgroup $C_G(H)$ of the complement is nilpotent of class $c$. It is proved that…

We establish the analogue of the Friedlander-Mazur conjecture for Teh's reduced Lawson homology groups of real varieties, which says that the reduced Lawson homology of a real quasi-projective variety $X$ vanishes in homological degrees…

It is shown that all nontrivial elements in higher $K$-groups of toric varieties over a class of regular rings are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality of vector…

We show that a differential algebraic group can be filtered by a finite subnormal series of differential algebraic groups such that successive quotients are almost simple, that is have no normal subgroups of the same type. We give a…

It was proved by Avramov and Buchweitz that if A is a commutative local complete intersection ring with finitely generated modules M and N, then the Ext groups between M and N vanish from some step if and only if the Ext groups between N…

We give a technical result that implies a straightforward necessary and sufficient conditions for a graph of groups with virtually cyclic edge groups to be one ended. For arbitrary graphs of groups, we show that if their fundamental group…

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…

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.

For most classical and similitude groups, we show that each element can be written as a product of two transformations that a) preserve or almost preserve the underlying form and b) whose squares are certain scalar maps. This generalizes…

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

We show that the group cohomology of torsion-free virtually polycyclic groups and the continuous cohomology of simply connected solvable Lie groups can be computed by the rational cohomology of algebraic groups. Our results are…