Related papers: Lamplighters over non-amenable groups are not stro…

We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…

We prove that for many nonamenable groups \Gamma, including all hyperbolic groups and all nontrivial free products, the left-right wreath product group G := (Z/2Z)^(\Gamma) \rtimes (\Gamma \times \Gamma) is W*-superrigid. This means that…

In this paper we study obstructions to presentability by products for finitely generated groups. Along the way we develop both the concept of acentral subgroups, and the relations between presentability by products on the one hand, and…

Let $\Gamma$ be a simplicial, finite, connected graph such that $\Gamma$ does not decompose as a nontrivial join. We prove that two notions of strong quasiconvexity and stability are equivalent in the right-angled Artin group $A_\Gamma$…

We define a sheaf of abelian groups whose cohomology is represented by the cotangent complex. We show how obstructions to some standard deformation problems arise as the classes of torsors under and gerbes banded by this sheaf.

In version v1 (under a different title) I was trying to give a new proof of Wedderburn's Little Theorem (WLT), stating that a finite dision ring is commutative, but I failed. So I had to withdraw the paper (version v2). Firstly I became…

We present a new proof, which is independent of the finite simple group classification and applies also to infinite groups, that quasiprimitive permutation groups of simple diagonal type cannot be embedded into wreath products in product…

We study one-variable equations over the lamplighter group $\MZ_2 \wr \MZ$. While the decidability of arbitrary equations over $L_2$ remains open, we prove that the Diophantine problem for single equations in one variable is decidable. Our…

This paper completely determines the non-amenability of the mapping class groups of infinite-type surfaces, the mapping class groups of locally finite infinite graphs of higher ranks, gives an example of non-amenable stabiliser of a point…

In this paper, a group is called weakly amenable if its left regular representation is not uniformly isolated from the trivial representation. First examples of finitely generated non-amenable weakly amenable groups are constructed.

We provide evidence for the Principle : Non-uniruled abelian fibrations are almost non-degenerate.

In regard to our recent studies of rings with (strongly, weakly) nil-clean-like properties, we explore in-depth both the structural and characterization properties of those rings whose elements that are not units are weakly nil-clean. Group…

We construct the first examples of residually finite amenable groups that are not Hilbert-Schmidt (HS) stable. We construct finitely generated, class 3 nilpotent by cyclic examples and solvable linear finitely presented examples. This also…

We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for probability measure preserving actions and rigidity of invariant…

Invariable generation is a topic that has predominantly been studied for finite groups. In 2014, Kantor, Lubotzky, and Shalev produced extensive tools for investigating invariable generation for infinite groups. Since their paper, various…

In this article we discuss cohomological obstructions to two kinds of group stability. In the first part, we show that residually finite groups $\Gamma$ which arise as fundamental groups of compact Riemannian manifolds with strictly…

A $\Lambda$-tree is a $\Lambda$-metric space satisfying three axioms (1), (2) and (3). We give a characterization of those ordered abelian groups $\Lambda$ for which axioms (1) and (2) imply axiom (3). As a special case, it follows that for…

We construct an explicit example of a stable bundle on the twistor space $\mathrm{Tw}(M)$ of a hyperk\"ahler manifold $M$ whose restrictions to all the fibres of the natural twistor projection $\pi : \mathrm{Tw}(M) \to \mathbb{CP}^1$ are…

The AMNM property for commutative Banach algebras is a form of Ulam stability for multiplicative linear functionals. We show that on any semilattice of infinite breadth, one may construct a weight for which the resulting weighted…

In this article we deduce an analogue of Quillen's Local-Global Principle for the elementary subgroup of the general quadratic group and the hermitian group. We show that the unstable K_1-groups of the hermitian groups are nilpotent by…