Related papers: Forty-plus annotated questions about large topolog…
This small survey of basic universal constructions related to the actions of topological groups on compacta is centred around a new result --- an intrinsic description of extremely amenable topological groups (i.e., those having a fixed…
This is an account of one man's view of the current perspective of theory of topological groups. We survey some recent developments which are, from our viewpoint, indicative of the future directions, concentrating on actions of topological…
We define and study notions of amenability and skew-amenability of continuous actions of topological groups on compact topological spaces. Our main motivation is the question under what conditions amenability of a topological group passes…
This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.
In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous…
We introduce the notion of soficity for locally compact groups and list a number of open problems.
We consider automorphism groups of some countably categorical structures and their precompact expansions. We prove that automorphism groups of omega-stable omega-categorical structures have metrizable universal minimal flows. We also study…
This survey/expository article covers a variety of topics related to the "topology at infinity" of noncompact manifolds and complexes. In manifold topology and geometric group theory, the most important noncompact spaces are often…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…
In this paper we collect some open set-theoretic problems that appear in the large-scale topology (called also Asymptology). In particular we ask problems about critical cardinalities of some special (large, indiscrete, inseparated) coarse…
We discuss some techniques related to equivariant compactifications of uniform spaces and amenability of topological groups. In particular, we give a new proof of a recent result by Glasner and Weiss describing the universal minimal flow of…
The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of…
We prove that if there are $\mathfrak c$ incomparable selective ultrafilters then, for every infinite cardinal $\kappa$ such that $\kappa^\omega=\kappa$, there exists a group topology on the free Abelian group of cardinality $\kappa$…
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
We study the topological structure and the topological dynamics of groups of homeomorphisms of scattered spaces. For a large class of them (including the homeomorphism group of any ordinal space or of any locally compact scattered space),…
Consider the following property of a topological group G: every continuous affine G-action on a Hilbert space with a bounded orbit has a fixed point. We prove that this property characterizes amenability for locally compact sigma-compact…
Groups of almost upper triangular infinite matrices with entries indexed by integers are studied. It is shown that, when the matrices are over a finite field, these groups admit a nondiscrete totally disconnected, locally compact group…
Every topological group $G$ has some natural compactifications which can be a useful tool of studying $G$. We discuss the following constructions: (1) the greatest ambit $S(G)$ is the compactification corresponding to the algebra of all…
We discuss definable compactifications and topological dynamics. For G a group definable in some structure M, we define notions of "definable" compactification of G and "definable" action of G on a compact space X (definable G-flow), where…