Related papers: H\"older maps from Euclidean spaces to Carnot grou…

We shall consider a locally compact groupoid endowed with a Haar system and having proper orbit space. We shall construct a groupoid C*-algebra which is independent of the Haar system (up to a *-isomorphism).

Given a semigroup of local homeomorphisms on a compact space X we consider the corresponding semigroup of *-endomorphisms on C(X) and discuss the possibility of extending it to an interaction group, a concept recently introduced by the…

We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of $C^k-$differentiable functions on…

A result due to M. Gromov states that any two finitely generated groups {\Gamma} and {\Lambda} are quasi-isometric if and only if they admit a topological coupling, i.e., a commuting pair of proper continuous cocompact actions…

We show, by an elementary and explicit construction, that the group of Hamiltonian diffeomorphisms of certain symplectic manifolds, endowed with Hofer's metric, contains subgroups quasi-isometric to Euclidean spaces of arbitrary dimension.

Consider a smooth map from a neighborhood of the origin in a real vector space to a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines passing through the origin to germs of Euclidean circles, or…

We consider mappings between Carnot groups. In this paper, which is a continuation of "Pansu pullback and rigidity of mappings between Carnot groups" (arXiv:2004.09271), we focus on Carnot groups which are nonrigid in the sense of…

We use Gromov's K--area to define a generalized homology theory on compact smooth manifolds. In fact, this theory collects obstructions to the enlargeability of the manifold and its nontrivial submanifolds. Moreover, using the K--area…

Let $G$ be second countable locally compact Hausdorff groupoid with a continuous Haar system. We remove the assumption of amenability in a theorem by Clark about GCR groupoid $C^*$-algebras. We show that if the groupoid $C^*$-algebra of $G$…

In his work on singularities, expanders and topology of maps, Gromov showed, using isoperimetric inequalities in graded algebras, that every real valued map on the $n$-torus admits a fibre whose homological size is bounded below by some…

\emph{Scalable spaces} are simply connected compact manifolds or finite complexes whose real cohomology algebra embeds in their algebra of (flat) differential forms. This is a rational homotopy invariant property and all scalable spaces are…

We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, consistently, there are many outer automorphisms.

This article investigates a few questions about orbits of local automorphisms in manifolds endowed with rigid geometric structures. We give sufficient conditions for local homogeneity in a broad class of such structures, namely Cartan…

Let $\Omega$ be a compact subset of $\mathbb{C}$ and let $A$ be a unital simple, separable $C^*$-algebra with stable rank one, real rank zero and strict comparison. We show that, given a Cu-morphism $\alpha:{\rm Cu}(C(\Omega))\to {\rm…

In this paper, we prove that the identity map for the smoothly bounded pseudoconvex domain of finite type in $\mathbb{C}^2$ extends to a bi-H\"{o}lder map between the Euclidean boundary and Gromov boundary. As an application, we show the…

Let $(G,\alpha)$ and $(H,\beta)$ be locally compact groupoids with Haar systems. We define a topological correspondence from $(G,\alpha)$ to $(H,\beta)$ to be a $G$-$H$-bispace $X$ on which $H$ acts properly and $X$ carries a continuous…

In this paper we establish a direct connection between stable approximate unitary equivalence for $*$-homomorphisms and the topology of the KK-groups which avoids entirely C*-algebra extension theory and does not require nuclearity…

We present an idea of unifying small scale (topology, proximity spaces, uniform spaces) and large scale (coarse spaces, large scale spaces). It relies on an analog of multilinear forms from Linear Algebra. Each form has a large scale…

Any $C^*$-algebra can be regarded as a generalization of locally compact, Hausdorff topological space $\mathcal X$. From the commutative commutative Gelfand-Na\u{\i}mark theorem it follows that the spectrum of any commutative $C^*$-algebra…

We prove that the group of contact diffeomorphisms is closed in the group of all diffeomorphisms in the C^0-topology. By Gromov's alternative, it suffices to exhibit a diffeomorphism that can not be approximated uniformly by contact…