Related papers: Continuous homomorphisms on piecewise absolutely c…

Let G be an abelian topological group. The symbol \hat{G} denotes the group of all continuous characters \chi : G --> T endowed with the compact open topology. A subset E of G is said to be qc-dense in G provided that \chi(E) \subseteq…

We show that any homomorphism from the homeomorphism group of a compact 2-manifold, with the compact-open topology, or equivalently, with the topology of uniform convergence, into a separable topological group is automatically continuous.

We address the (pointed) homotopy of crossed module morphisms in modified categories of interest; which generalizes the groups and various algebraic structures. We prove that, the homotopy relation gives rise to an equivalence relation;…

We show that every abstract homomorphism $\varphi$ from a locally compact group $L$ to a graph product $G_\Gamma$, endowed with the discrete topology, is either continuous or $\varphi(L)$ lies in a 'small' parabolic subgroup. In particular,…

Given an algebraic theory $\ct$, a homotopy $\ct$-algebra is a simplicial set where all equations from $\ct$ hold up to homotopy. All homotopy $\ct$-algebras form a homotopy variety. We give a characterization of homotopy varieties…

Let the measure algebra of a topological group be equipped with the topology of uniform convergence on bounded right uniformly equicontinuous sets of functions. Convolution is separately continuous on the measure algebra, and it is jointly…

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…

We show that continuous group homomorphisms between unitary groups of unital C*-algebras induce maps between spaces of continuous real-valued affine functions on the trace simplices. Under certain $K$-theoretic regularity conditions, these…

Let $A$ be a unital simple separable exact C$^*$-algebra which is approximately divisible and of real rank zero. We prove that the set of positive elements in $A$ with a fixed Cuntz class is path connected. This result applies in particular…

We extend the proof of automatic continuity for homeomorphism groups of manifolds to non-compact manifolds and manifolds with marked points and their mapping class groups. Specifically, we show that, for any manifold $M$ homeomorphic to the…

We establish the continuous homotopy invariance of bivariant local cyclic homology on the category of all \sigma-C^*-algebras. The argument relies vitally on an isomorphism between the smooth and continuous cylinder constructions using a…

For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative…

For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative…

Let $\text{Homeo}_{+}(\mathbb{S}^1)$ denote the group of orientation preserving homeomorphisms of the circle $\mathbb{S}^1$. A subgroup $G$ of $\text{Homeo}_{+}(\mathbb{S}^1)$ is tightly transitive if it is topologically transitive and no…

Let $A(G)$ and $B(H)$ be the Fourier and Fourier-Stieltjes algebras of locally compact groups $G$ and $H$, respectively. Ilie and Spronk have shown that continuous piecewise affine maps $\alpha: Y \subseteq H\rightarrow G$ induce completely…

This paper concerns rigidity of the mapping class groups. We show that any homomorphism $\phi:{\rm Mod}_g\to {\rm Mod}_h$ between mapping class groups of closed orientable surfaces with distinct genera $g>h$ is trivial if $g\geq 3$ and has…

This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups $H < {\rm GL}(3,\mathbb{R})$ that give rise to a continuous wavelet transform with associated irreducible quasi-regular…

Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the…

We produce affine interval exchange transformations (AIETs) which are topologically conjugated to (standard) interval exchange maps (IETs) via a singular conjugacy, i.e. a diffeomorphism $h$ of $[0,1]$ which is $C^0$ but not $C^1$ and such…

Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways. For the first of these, we show that…