Related papers: On the topological essential range and regularity …
We prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language. We also study the cohomology of the…
This paper explores the concept of topological transitivity in nonautonomous dynamical systems, which are defined as sequences of continuous maps from a compact metric space to itself. It investigates various conditions (including…
We investigate small $p$-groups with cohomology rings of depth higher than predicted by Duflot's theorem. In these groups, a sampling would suggest several naive conjectures about the degrees of the additional regular sequence elements. We…
Multilayer networks have permeated all the sciences as a powerful mathematical abstraction for interdependent heterogenous complex systems such as multimodal brain connectomes, transportation, ecological systems, and scientific…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
We propose a homology theory for locally compact spaces with ends in which the ends play a special role. The approach is motivated by results for graphs with ends, where it has been highly successful. But it was unclear how the original…
We study relatively minimal subgroups in topological groups. We find, in particular, some natural relatively minimal subgroups in unipotent groups which are defined over "good" rings. By "good" rings we mean archimedean absolute valued (not…
In this m\'emoire we study quasiperiodic cocycles in semi-simple compact Lie groups. For the greatest part of our study, we will focus ourselves to one-frequency cocyles. We will prove that $C^{\infty}$ reducible cocycles are dense in the…
The positive cohomology groups of a finite group acting on a ring vanish when the ring has a norm-one element. In this note we give explicit homotopies on the level of cochains when the group is cyclic, which allows us to express any…
We introduce a fairly general concept of functional equation for $k$-tuples of functions $f_1,\dots,f_k\colon X \to Y$ between arbitrary sets. The homomorphy equations for mappings between groups and other algebraic systems, as well as…
We study properties of the Weyl pseudometric associated with an action of a countable amenable group on a compact metric space. We prove that the topological entropy and the number of minimal subsets of the closure of an orbit are both…
This paper studies Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all classes in that theory have representatives with considerable extra…
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 paper defines and discusses the dimension notion of topological slow entropy of any subset for Z^d actions. Also, the notion of measure-theoretic slow entropy for Z^d actions is presented, which is modified from Brin and Katok [2].…
A cocycle category H(X,Y) is defined for objects X and Y in a model category, and it is shown that the set of morphisms [X,Y] is isomorphic to the set of path components of H(X,Y) provided the ambient model category is right proper and…
Without leaving finite mathematics and using finite topological spaces only, we give a definition of homeomorphisms of finite abstract simplicial complexes or finite graphs. Besides exploring the definition in various contexts, we add some…
In this thesis, we provide an initial investigation into bounds for topological entropy of switched linear systems. Entropy measures, roughly, the information needed to describe the behavior of a system with finite precision on finite time…
We investigate to what extent a minimal topological dynamical system is uniquely determined by a set of return times to some open set. We show that in many situations this is indeed the case as long as the closure of this open set has no…
This paper is devoted to problems stated by Z. Zhou and F. Li in 2009. They concern relations between almost periodic, weakly almost periodic, and quasi-weakly almost periodic points of a continuous map f and its topological entropy. The…
We interpret the probabilistic notion of unimodularity for measures on the space of rooted locally finite connected graphs in terms of the theory of measured equivalence relations. It turns out that the right framework for this consists in…