Related papers: Survey on the Farrell-Jones Conjecture

In this note we formulate a conjecture about two group ring identities and prove that it would imply the Alon-Jaeger-Tarsi conjecture.

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 show that the Fibered Isomorphism Conjecture (FIC) of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for the fundamental groups of a large class of 3-manifolds. We also prove that if the FIC is…

The paper discusses the Andrews-Curtis graph of a normal subgroup N in a group G. The vertices of the graph are k-tuples of elements in N which generate N as a normal subgroup; two vertices are connected if one them can be obtained from…

The topic of this survey is the phenomenon of fibring over the circle for manifolds, and its group-theoretic twin, algebraic fibring. We will discuss the state of the art, and explain briefly some of the ideas behind the more recent…

The K-theory of a functor may be viewed as a relative version of the K-theory of a ring. In the case of a Galois extension of a number field F/L with rings of integers A/B respectively, this K-theory of the "norm functor" is an extension of…

Long and thin covers of flow spaces are important ingredients in the proof of the Farrell--Jones conjecture for certain classes of groups, like hyperbolic and CAT(0)-groups. In this paper we provide an alternative construction of such…

The aim of this survey is to present applications of covering techniques in the theory of Krull-Gabriel dimension. We start with recalling fundamental facts of the classical covering theory of quivers and locally bounded categories. Then we…

A survey of the applications of the noncommutative Cohn localization of rings to the topology of manifolds with infinite fundamental group, with particular emphasis on the algebraic K- and L-theory of generalized free products.

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…

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…

Algebraic K-theory is the stable homotopy theory of homotopy theories, and it interacts with algebraic structures accordingly. In particular, we prove the Deligne Conjecture for algebraic K-theory.

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

Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…

We introduce and analyze the concept of an assembly map from the original homotopy theoretic point of view. We give also interpretations in terms of surgery theory, controlled topology and index theory. The motivation is that prominent…

One important class of tools in the study of the connections between algebraic and topological structures are the "Banach-Stone type theorems", which describe algebraic isomorphisms of algebras (or groups, lattices, etc.) of functions in…

We introduce a coarse flow space for relatively hyperbolic groups and use it to verify a regularity condition for the action of relatively hyperbolic groups on their boundaries. As an application the Farrell-Jones Conjecture for relatively…

Equivariant homotopy methods developed over the last 20 years lead to recent breakthroughs in the Borel isomorphism conjectures for Loday assembly maps in K- and L-theories. An important consequence of these algebraic conjectures is the…

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…

We give a survey of the theory of surface braid groups and the lower algebraic K-theory of their group rings. We recall several definitions and describe various properties of surface braid groups, such as the existence of torsion,…