Related papers: The Farrell-Jones Conjecture for normally poly-fre…

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…

In this paper we show that the Farrell-Jones isomorphism conjectures are inherited in group extensions for assembly maps in algebraic $K$-theory and $L$-theory with twisted coefficients.

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 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…

We prove that even Artin groups of FC type are poly-free and residually finite.

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. Using controlled category theory we are able to translate this conjecture for asymptotically faithful…

We propose two definitions of configuration Lie groupoids and in both the cases we prove a Fadell-Neuwirth type fibration theorem for a class of Lie groupoids. We show that this is the best possible extension, in the sense that, for the…

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 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…

In this paper we formulate and lay the foundations for the K-theoretic Farrell-Jones Conjecture for the Hecke algebra of totally disconnected groups. The main result of his paper is the proof that it passes to closed subgroups. Moreover, we…

Motivated by the Farrell-Jones Conjecture for group rings, we formulate the $\mathcal{C}$op-Farrell-Jones Conjecture for the K-theory of Hecke algebras of td-groups. We prove this conjecture for (closed subgroups of) reductive p-adic groups…

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…

We prove the Farrell-Jones Conjecture for mapping class groups. The proof uses the Masur-Minsky theory of the large scale geometry of mapping class groups and the geometry of the thick part of Teichmueller space. The proof is presented in…

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 conjecture that the word problem of Artin-Tits groups can be solved without introducing trivial factors ss^{-1} or s^{-1}s. Here we make this statement precise and explain how it can be seen as a weak form of hyperbolicity. We prove the…

Consider a totally disconnected group G, which is covirtually cyclic, i.e., contains a normal compact open subgroup L such that G/L is infinite cyclic. We establish a Wang sequence, which computes the algebraic K-groups of the Hecke algebra…

We develop general methods to compute the algebraic $K$-theory of crossed products by Bernoulli shifts on additive categories. From this we obtain a $K$-theory formula for regular group rings associated to wreath products of finite groups…

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…