Related papers: Farrell-Jones Conjecture for free-by-cyclic groups

We give a simple proof of the Lalonde-McDuff conjecture for aspherical manifolds.

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…

We prove a generalization of Fulton's conjecture which relates intersection theory on an arbitrary flag variety to invariant theory.

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

This paper is devoted to the proof of the property of order separability for free product of free groups with maximal cyclic amalgamated subgroups.

We prove a generalized Fej\'er's theorem for locally compact groups.

We show that the holomorph of the free group on two generators satisfies the Farrell-Jones Fibered Isomorphism Conjecture. As a consequence, we show that the lower K-theory of the above group vanishes.

We use controlled topology applied to the action of the infinite dihedral group on a partially compactified plane and deduce two consequences for algebraic K-theory. The first is that the family in the K-theoretic Farrell-Jones conjecture…

We extend the class of abelian groups for which a conjecture of Asai and Yoshida on the number of crossed homomorphisms holds. We also prove a general result which connects certain problems concerning divisibility in groups to the…

The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent…

We give a geometric proof of a well known theorem that describes splittings of a free group as an amalgamated product or HNN extension over the integers. The argument generalizes to give a similar description of splittings of a virtually…

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…

We discuss an analogon to the Farrell-Jones Conjecture for homotopy algebraic K-theory. In particular, we prove that if a group G acts on a tree and all isotropy groups satisfy this conjecture, then G satisfies this conjecture. This result…

The Farrell-Jones and the Baum-Connes Conjecture say that one can compute the algebraic K- and L-theory of the group ring and the topological K-theory of the reduced group C^*-algebra of a group G in terms of these functors for the…

We discuss some new results concerning Gap Conjecture on group growth and present a reduction of it (and its *-version) to several special classes of groups. Namely we show that its validity for the classes of simple groups and residually…

We show that a free-by-cyclic group with a polynomially growing monodromy is subgroup separable exactly when it is virtually $F_n \times \mathbb{Z}$. We also prove that random deficiency 1 groups are not subgroup separable with positive…

We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed subgroups of free group automorphisms, and one…

In this paper, we focus on Oliver's $p$-group conjecture. We use elementary method to prove that Oliver's $p$-group conjecture holds for Sylow $p$-subgroups of unitary groups.

We show that the group $\langle a,b,c,t : a^t=b,b^t=c,c^t=ca^{-1} \rangle$ is profinitely rigid amongst free-by-cyclic groups, providing the first example of a hyperbolic free-by-cyclic group with this property.

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…