Related papers: Homomorphisms into totally disconnected, locally c…
We prove that arbitrary homomorphisms from one of the groups ${\rm Homeo}(\ca)$, ${\rm Homeo}(\ca)^\N$, ${\rm Aut}(\Q,<)$, ${\rm Homeo}(\R)$, or ${\rm Homeo}(S^1)$ into a separable group are automatically continuous. This has consequences…
We define a local Sylow subgroup of a totally disconnected, locally compact group G to be a maximal pro-p subgroup of an open compact subgroup of G. We use these subgroups to define the p-localisation of G, a locally virtually pro-p group…
Generalizing results from \cite{DTk,DU} we study the fine structure of locally minimal (locally) precompact Abelian groups (these are the locally essential subgroups $G$ of LCA groups $L$, i.e., such that $G$ non-trivially meets all…
The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…
An image is here defined to be a set which is either open or closed and an image transformation is structure preserving in the following sense: It corresponds to an algebra homomorphism for each singly generated algebra. The results extend…
According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism G^ --> D^ of the dual groups is a topological isomorphism. We introduce four conditions on D…
If $G$ is a finite group or a torus, it is known that there is an isomorphism between the Grothendieck group of homotopy representations and that of generalized homotopy representations for $G$. We prove that there is such an isomorphism…
To any dg-category $T$ (over some base ring $k$), we define a $D^{-}$-stack $\mathcal{M}_{T}$ in the sense of \cite{hagII}, classifying certain $T^{op}$-dg-modules. When $T$ is saturated, $\mathcal{M}_{T}$ classifies compact objects in the…
We prove that a group homomorphism $\varphi\colon L\to G$ from a locally compact Hausdorff group $L$ into a discrete group $G$ either is continuous, or there exists a normal open subgroup $N\subseteq L$ such that $\varphi(N)$ is a torsion…
Let $\mathcal C$ be a subcategory of the category of topologized semigroups and their partial continuous homomorphisms. An object $X$ of the category ${\mathcal C}$ is called ${\mathcal C}$-closed if for each morphism $f:X\to Y$ of the…
We classify all compact simply connected homogeneous CR manifolds $M$ of codimension one and with non-degenerate Levi form up to CR equivalence. The classification is based on our previous results and on a description of the maximal…
Two graphs are homomorphism indistinguishable over a graph class $\mathcal{F}$, denoted by $G \equiv_{\mathcal{F}} H$, if $\operatorname{hom}(F,G) = \operatorname{hom}(F,H)$ for all $F \in \mathcal{F}$ where $\operatorname{hom}(F,G)$…
Let $f:G\rightarrow H$ be a homomorphism of groups, we construct a topological space $X_f$ such that its group of homeomorphisms is isomorphic to $G$, its group of homotopy classes of self-homotopy equivalences is isomorphic to $H$ and the…
Counting homomorphisms from a graph $H$ into another graph $G$ is a fundamental problem of (parameterized) counting complexity theory. In this work, we study the case where \emph{both} graphs $H$ and $G$ stem from given classes of graphs:…
A fundamental result of Banyaga states that the Hamiltonian diffeomorphism group of a closed symplectic manifold is perfect. We refine this result by proving that, locally in the $C^\infty$ topology, the number of commutators needed to…
Let G be a finitely generated relatively hyperbolic group. We show that if no peripheral subgroup of G is hyperbolic relative to a collection of proper subgroups, then the fixed subgroup of every automorphism of G is relatively quasiconvex.…
We prove the following result: Let K be a lattice, let D be a distributive lattice with zero, and let $\phi$: Con K $\to$ D be a {∨, 0}-homomorphism, where Conc K denotes the {∨, 0}-semilattice of all finitely generated…
We prove that an arbitrary compact metrizable group can be realized as the automorphism group of a graphing; this is a continuous analogue to Frucht's theorem recovering arbitrary finite groups are automorphism groups of finite graphs. The…
A group homomorphism eta:A-> H is called a localization of A if every homomorphism phi:A-> H can be `extended uniquely' to a homomorphism Phi:H-> H in the sense that Phi eta = phi. This categorical concepts, obviously not depending on the…
Mapping class groups of locally finite graphs are the analogue of those of infinite-type surfaces, and serve as a "big" version of $\text{Out}(F_n)$. In this paper, we investigate which of these mapping class groups have a dense conjugacy…