Related papers: Locally normal subgroups of simple locally compact…

We prove that, under mild assumptions, a lattice in a product of semi-simple Lie group and a totally disconnected locally compact group is, in a certain sense, arithmetic. We do not assume the lattice to be finitely generated or the ambient…

We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.

We present some basic results on a natural Poisson structure on any compact symmetric space. The symplectic leaves of this structure are related to the orbits of the corresponding real semisimple group on the complex flag manifold.

Let $G$ be a noncompact real algebraic group and $\G<G$ a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of $G$ or $\G$ on a compact manifold which admits a smooth deformation. We…

We generalize the concepts of locally presentable and accessible categories. Our framework includes such categories as small presheaves over large categories and ind-categories. This generalization is intended for applications in the…

In this paper we present local Sternberg conjugation theorems near attracting fixed points for lattice systems. The interactions are spatially decaying and are not restricted to finite distance. The conjugations obtained retain the same…

We determine the normalizer in $SL_{2}(\mathbb{R})$ of several families of congruence subgroups of $SL_{2}(\mathbb{Z})$. In addition, we show how these tools can be used to evaluate the groups of automorphisms and the discriminant kernels…

Recently we have shown a structure theorem for locally compact groups of polynomial growth. We give now some applications on various growth functions and relations to FC-G - series. In addition, we show some results on related classes of…

In this note we classify all homogeneous spaces $G/H$ admitting a $G$-invariant $G_2$-structure, assuming that $G$ is a compact Lie group and $G$ acts effectively on $G/H$. They include a subclass of all homogeneous spaces $G/H$ with a…

In this note we study the finite groups whose subgroup lattices are dismantlable.

We study hamiltonian actions of compact groups in the presence of compatible involutions. We show that the lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces…

We determine which of the finite-type Artin groups are locally indicable, and compute presentations for their commutator subgroups.

We give a normalizer decomposition for a p-local compact group (S, F, L) that describes |L| as a homotopy colimit indexed over a finite poset. Our work generalizes the normalizer decompositions for finite groups due to Dwyer, for p-local…

Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product C*-algebras for non-supramenable groups. In particular, stable Kirchberg…

We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mainly on compact quantum groups we consider the question…

We present a new method of establishing a bijective correspondence - in fact, a lattice isomorphism - between action- and coaction-invariant ideals of C*-algebras and their crossed products by a fixed locally compact group. It is known that…

We show a rigidity result for subfactors that are normalized by a representation of a lattice $\Gamma$ in a higher rank simple Lie group with trivial center into a finite factor. This implies that every subfactor of $L\Gamma$ which is…

We investigate a family of groups acting on a regular tree, defined by prescribing the local action almost everywhere. We study lattices in these groups and give examples of compactly generated simple groups of finite asymptotic dimension…

The Kechris-Pestov-Todorcevic correspondence connects extreme amenability of non-Archimedean Polish groups with Ramsey properties of classes of finite structures. The purpose of the present paper is to recast it as one of the instances of a…

It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…