Related papers: Nilpotent extensions of minimal homeomorphisms

Let $G/P$ be a rational homogeneous space (not necessarily irreducible) and $x_0\in G/P$ be the point at which the isotropy group is $P$. The $G$-translates of the orbit $Qx_0$ of a parabolic subgroup $Q\subsetneq G$ such that $P\cap Q$ is…

Ring epimorphisms often induce silting modules and cosilting modules, termed minimal silting or minimal cosilting. The aim of this paper is twofold. Firstly, we determine the minimal tilting and minimal cotilting modules over a tame…

We show that given a compact minimal system $(X,g)$ and an element $h$ of the topological full group $\tau[g]$ of $g$, then the infinite orbits of $h$ admit a locally constant orientation with respect to the orbits of $g$. We use this to…

We study when a piecewise full group (a.k.a. topological full group) of homeomorphisms of the Cantor space $X$ can be given a non-discrete totally disconnected locally compact (t.d.l.c.) topology and give a criterion for the alternating…

Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that…

In this paper we study perturbations of constant cocycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's cocycle superrigidity theorems implies that the perturbed…

We prove topological regularity results for isoperimetric sets in PI spaces having a suitable deformation property, which prescribes a control on the increment of the perimeter of sets under perturbations with balls. More precisely, we…

We prove that various classical conformal diffeomorphism groups, which are known to be essential [1], are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of a cohomological…

In this article we consider homeomorphisms of the open annulus $\mathbb{A}=\mathbb{R}/\mathbb{Z}\times \mathbb{R}$ which are isotopic to the identity and preserve a Borel probability measure of full support, focusing on the existence of…

Continuing our research on extensions of locally compact quantum groups, we give a classification of all cocycle matched pairs of Lie algebras in small dimensions and prove that all of them can be exponentiated to cocycle matched pairs of…

The necessity of a theory of General Topology and, most of all, of Algebraic Topology on locally finite metric spaces comes from many areas of research in both Applied and Pure Mathematics: Molecular Biology, Mathematical Chemistry,…

An area-preserving homeomorphism isotopic to the identity is said to have rational rotation direction if its rotation vector is a real multiple of a rational class. We give a short proof that any area-preserving homeomorphism of a compact…

We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or…

Various theorems on convergence of general space homeomorphisms are proved and, on this basis, theorems on convergence and compactness for classes of the so-called ring $Q$--homeomorphisms are obtained. In particular, it was established by…

A Hausdorff topological group is called minimal if it does not admit a strictly coarser Hausdorff group topology. This paper mostly deals with the topological group $H_+(X)$ of order-preserving homeomorphisms of a compact linearly ordered…

Let P be a closed triangulated manifold, dim P=n. We consider the group of simplicial 1-chains C_1(P) and the homology group H_1(P). We also use some nonnegative weighting function L on C_1(P). For any homological class from H_1(P) method…

This article deals with topological assumptions under which the minimal volume entropy of a closed manifold, and more generally of a finite simplicial complex, vanishes or is positive. In the first part of the article, we present…

We use cross ratios to describe second real continuous bounded cohomology for locally compact topological groups. We also derive a rigidity result for cocycles with values in the isometry group of a proper hyperbolic geodesic metric space.

The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite CW-complexes. We show that these obstructions do not hold for more general spaces. More…

We show the following geometric generalization of a classical theorem of W.H. Gottschalk and G.A. Hedlund: a skew action induced by a cocycle of (affine) isometries of a Hilbert space over a minimal dynamics has a continuous invariant…