Related papers: Open mappings of locally compact groups

We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…

We conjecture that the automorphism group of a topological parallelism on real projective 3-space is compact. We prove that at least the identity component of this group is, indeed, compact.

This note is devoted to proving the following result: given a compact metrizable group G, there is a compact metric space K such that G is isomorphic (as a topological group) to the isometry group of K.

The aim of this short paper is to summarize my recent preprint (arXiv:1209.1112), in which I proposed a novel and probably controversial view about cognitive mapping; that is, the image of the city out of the underlying scaling of city…

In this short survey article, we try to list maximum number of known results on class preserving automorphisms of finite $p$-groups. We conclude the survey with some interesting (at least for the author) open problems on this topic.

A generalization of the notion of an $\infty$-category is presented, allowing for ($\infty$-)cat(egorie)s that may have non-invertible higher morphisms.

For any $C\in[0,\infty]$ a compact group automorphism $T:X\to X$ is constructed with the property that $$ \frac{1}{n}\log|\{x\in X\mid T^n(x)=x\}|\longrightarrow C. $$ This may be interpreted as a combinatorial analogue of the (still open)…

We study the centraliser of locally compact group extensions of ergodic probability preserving transformations. New methods establishing ergodicity of group extensions are introduced, and new examples of squashable and non-coalescent group…

The paper deals with continuous and compact mappings generated by the Fourier transform between distinguished function spaces on $\mathbb{R}^n$. The degree of compactness will be measured in terms of related entropy numbers. We are more…

This short note collects three open questions on cut groups (a class of groups generalizing rational groups).

In this paper we give sufficient conditions under which a subsemigroup of a topological group is a subgroup, adding to the results given in \cite{Kosh, can, axioms, forum, Hof, cc, locally} where conditions exist (such as locally…

This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…

We show that the space of expanding maps contains an open and dense set where smooth conjugacy classes of expanding maps are determined by the values of the Jacobians of return maps at periodic points.

Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…

Our goal is to provide a survey of some topics in quasiconformal analysis of current interest. We try to emphasize ideas and leave proofs and technicalities aside. Several easily stated open problems are given. Most of the results are joint…

We classify the locally compact second-countable (l.c.s.c.) groups $A$ that are abelian and topologically characteristically simple. All such groups $A$ occur as the monolith of some soluble l.c.s.c. group $G$ of derived length at most $3$;…

In this article, we describe all the group morphisms from the group of compactly-supported homeomorphisms isotopic to the identity of a manifold to the group of homeomorphisms of the real line or of the circle.

We develop a theory of umkehr maps for twisted generalized homology theories. In this theory, interesting umkehr maps, including generalizations of important classical ones, are induced by cartesian morphisms of a certain category opfibred…

This is a biased survey for the Johnson homomorphisms of the automorphism groups of free groups. We just exposit some well known facts and recent developments for the Johnson homomorphisms and its related topics.

Through careful analysis of types inspired by [AGTW21] we characterize a notion of definable compactness for definable topologies in general o-minimal structures, generalizing results from [PP07] about closed and bounded definable sets in…