Related papers: On the isomorphism conjecture for groups acting on…

We establish the existence of Springer isomorphisms for reductive group schemes over general base schemes. For this, we first study centralizers of fiberwise regular sections of reductive group schemes, and we establish their flatness in…

We introduce the notion of \textit{fibered lifted partially hyperbolic diffeomorphisms} and we prove that any partially hyperbolic diifeomorphism isotopic to a fibered lifted one where the isotopy take place inside partially hyperbolic…

Let Gamma be a connected, locally finite graph of finite tree width and G be a group acting on it with finitely many orbits and finite node stabilizers. We provide an elementary and direct construction of a tree T on which G acts with…

We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro-$\mathcal{C}$ completions of the…

For a closed and orientable surface of genus at least 2, we prove the surface group extensions of the stabilizers of multicurves are hierarchically hyperbolic groups. This answers a question of Durham, Dowdall, Leininger, and Sisto. We also…

In this paper a Bass-Serre theory in the groupoid setting is developed and a structure theorem is established. Any groupoid action without inversion of edges on a forest induces a graph of groupoids, while any graph of groupoids satisfying…

This paper and its companion arXiv:0911.3173 have been replaced by arXiv:1602.05139. We define the compatibility JSJ tree of a group G over a class of subgroups. It exists whenever G is finitely presented and leads to a canonical tree (not…

We prove that a permutation group in which different finite sets have different stabilizers cannot satisfy any group law. For locally compact topological groups with this property we show that almost all finite subsets of the group generate…

Bowditch's JSJ tree for splittings over 2-ended subgroups is a quasi-isometry invariant for 1-ended hyperbolic groups which are not cocompact Fuchsian. Our main result gives an explicit, computable "visual" construction of this tree for…

This work is a continuation of Automorphisms of $K$-groups I, P. Flavell, preprint. The main object of study is a finite $K$-group $G$ that admits an elementary abelian group $A$ acting coprimely. For certain group theoretic properties…

We prove a criterion for the geometric and algebraic finiteness properties of vertex stabilisers of $G$-CW-complexes, given the finiteness properties of the group $G$ and of the stabilisers of positive dimensional cells. This generalises a…

We are interested in finite groups acting orientation-preservingly on 3-manifolds (arbitrary actions, ie not necessarily free actions). In particular we consider finite groups which contain an involution with nonempty connected fixed point…

This paper is concerned with the Laitinen Conjecture. The conjecture predicts an answer to the Smith question which reads as follows. Is it true that for a finite group acting smoothly on a sphere with exactly two fixed points, the tangent…

It is shown that for any action of a finitely presented group $G$ on an $\R$-tree, there is a decomposition of $G$ as the fundamental group of a graph of groups related to this action. If the action of $G$ on $T$ is non-trivial, i.e. there…

In this paper we prove that given a non-isotrivial family of hyperbolic curves in positive characteristic, the isomorphism type of the geometric fundamental group is not constant on the fibres of the family.

We prove the Baum--Connes conjecture with arbitrary coefficients for some classes of groups: (1) Linear algebraic groups over a non-archimedean local field. (2) Linear algebraic groups over the adeles of a global field k, provided that at…

Sp\"ath showed that the Alperin-McKay conjecture in the representation theory of finite groups holds if the so-called inductive Alperin-McKay condition holds for all finite simple groups. In a previous article, we showed that the…

In this note, we prove the K- and L-theoretic Farrell-Jones Conjecture with coefficients in an additive category for fundamental groups of graphs of virtually cyclic groups.

We show that tree almost automorphism groups, including Neretin groups, satisfy the analogue of the $F_\infty$-finiteness condition in the world of totally disconnected groups: They possess a cellular action on a contractible cellular…

The Isomorphism Conjecture is a conceptional approach towards a calculation of the algebraic K-theory of a group ring RG, where G is an infinite group. In this paper we prove the conjecture in dimensions n<2 for fundamental groups of closed…