相关论文: On proofs of the Farrell-Jones Conjecture
These extended notes are based on a series of six lectures presented at the summer school ``Cohomology of groups and algebraic $K$-theory'' which took place in Hangzhou, China from July 1 until July 12 in 2007. They give an introduction to…
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 prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for virtually solvable groups.
We show how the existing proof of the Farrell-Jones Conjecture for virtually poly-$\mathbb{Z}$-groups can be improved to rely only on the usual inheritance properties in combination with transfer reducibility as a sufficient criterion for…
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 K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for GL_n(Z).
We generalize the proof of the Farrell-Jones conjecture for CAT(0)-groups to a larger class of groups in particular also containing all hyperbolic groups. This way we give a unified proof for both classes of groups.
We prove the K-theoretic Farrell-Jones conjecture with (twisted) coefficients for CAT(0)-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.
This paper contains the results of my PhD-thesis. I will show the K- and L-theoretic Farrell-Jones conjecture (FJC) for the general linear groups over the rationals and over the rational functions over a finite field. This especially…
This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…
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…
New cases of the multiplicity conjecture are considered.
We prove the Farrell-Jones conjecture for free-by-cyclic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture.
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…
This note gives an informal overview of the proof in our paper "Borel Conjecture and Dual Borel Conjecture", see arXiv:1105.0823.
We show that the Farrell-Jones Conjecture holds for fundamental groups of graphs of groups with abelian vertex groups. As a special case, this shows that the conjecture holds for generalized Baumslag-Solitar groups.
Notes of an introductory course given at the conference "Torsors: Theory and Applications" in Edinburgh, January 2011.
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 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…