Related papers: Forty-plus annotated questions about large topolog…

The article is devoted to the question whether the orbit space of a compact linear group is a topological manifold and a homological manifold. In the paper, the case of a simple three-dimensional group is considered. An upper bound is…

We provide an estimate of the amenable category of oriented closed connected complete affine manifolds whose fundamental group contains an infinite amenable normal subgroup. As an application we show that all such manifolds have zero…

We show that there are locally compact spaces that can be condensed onto separable spaces but not onto compact separable spaces. We also show that for every cardinal $\kappa$ there is a locally compact topological group of cardinality…

We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.

The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous…

We study amenability of definable and topological groups. Among our main technical tools is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and some results around measures. As an application we…

We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular…

Assuming the existence of $\mathfrak c$ incomparable selective ultrafilters, we classify the non-torsion Abelian groups of cardinality $\mathfrak c$ that admit a countably compact group topology. We show that for each $\kappa \in [\mathfrak…

A survey of finite group actions on symplectic 4-manifolds is given with a special emphasis on results and questions concerning smooth or symplectic classification of group actions, group actions and exotic smooth structures, and…

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…

For locally compact groups amenability and Kazhdan's property (T) are mutually exclusive in the sense that a group having both properties is compact. This is no longer true for more general Polish groups. However, a weaker result still…

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications.

We construct equilibrium states, including measures of maximal entropy, for a large (open) class of non-uniformly expanding maps on compact manifolds. Moreover, we study uniqueness of these equilibrium states, as well as some of their…

We introduce an Ulam-type stability condition for positive definite maps defined on a countable group and prove that this condition characterizes amenability.

By considering appropriate finite covering spaces of closed non-orientable surfaces, we construct linear representations of their mapping class group which have finite index image in certain big arithmetic groups.

Our purpose is to study in the setting of locally compact groupoids the analogues of the well-known equivalent definitions of exactness for discrete groups. Our best results are obtained for a class of \'etale groupoids that we call inner…

The relation between manifold topology, observables and gauge group is clarified on the basis of the classification of the representations of the algebra of observables associated to positions and displacements on the manifold. The guiding,…

Our aim is to solve a quite old question on the difference between expandability and compact expandability. Toward this, we further investigate the logic of countable cofinality.

We define and study the class of inner ultrahomogeneous groups, which includes Hall's universal group and the universal locally recursively presentable group. We provide simple criteria for ample generic automorphisms, straight maximality,…

We discuss a number of topics in the area of conformally compact Einstein metrics, mostly centered around the global existence question of finding such metrics with an arbitrarily prescribed conformal infinity. The paper is partly a survey…