相关论文: Symmetric products of Erd\H{o}s space and complete…

Let $X$ be an infinite compact metric space with finite covering dimension and let $\alpha, \beta : X\to X$ be two minimal homeomorphisms. We prove that the crossed product $C^*$-algebras $C(X)\rtimes_\alpha\Z$ and $C(X)\rtimes_\belta\Z$…

Let ${\rm Fin}(X)$ be the hyperspace consisting of non-empty finite subsets of a space $X$ endowed with the Vietoris topology. In this paper, we characterize a metrizable space $X$ whose hyperspace ${\rm Fin}(X)$ is homeomorphic to the…

In this expository paper, we provide an intuition and illustration-driven overview of two recent results that tie the dynamics of certain homeomorphisms of infinite-type surfaces, called end-periodic homeomorphisms, to the geometry of their…

We study the homology of Riemannian manifolds of finite volume that are covered by an $r$-fold product $(\mathbb{H}^2)^r = \mathbb{H}^2 \times \ldots \times \mathbb{H}^2$ of hyperbolic planes. Using a variation of a method developed by…

A theorem by Norman L. Noble from 1970 asserts that every product of completely regular, locally pseudo-compact k_R-spaces is a k_R-space. As a consequence, all direct products of locally compact Hausdorff spaces are k_R-spaces. We provide…

According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex…

In this paper, we compute the cohomology ring of all homology split polyhedral product spaces and the cohomology algebra over a field of all polyhedral product spaces. As an application, we give two polyhedral product spaces such that all…

In this work, the warped product of Hamilton spaces is introduced and it is shown that these spaces obtain Hamiltonian structure as well. Then, the geometric properties of warped product Hamilton spaces such as their nonlinear connections…

An intrinsic definition in terms of conformal capacity is proposed for the conformal type of a Carnot--Carath\'eodory space (parabolic or hyperbolic). Geometric criteria of conformal type are presented. They are closely related to the…

In this paper, we study biharmonic hypersurfaces in Einstein manifolds. Then, we determine all the biharmonic hypersurfaces in irreducible symmetric spaces of compact type which are regular orbits of commutative Hermann actions of…

We prove that manifolds admitting a Riemannian metric for which products of harmonic forms are harmonic satisfy strong topological restrictions, some of which are akin to properties of flat manifolds. Others are more subtle, and are related…

We prove that the upper metric mean dimension of $C^0$-generic homeomorphisms, acting on a compact smooth boundaryless manifold with dimension greater than one, coincides with the dimension of the manifold. In the case of continuous…

Let $S$ be a complete flat surface, such as the Euclidean plane. We determine the homeomorphism class of the space of all curves on $S$ which start and end at given points in given directions and whose curvatures are constrained to lie in a…

This paper exhibits a multiplicative and minimal cellular complex which allows explicit and complete (co)homological calculations for the symmetric products of a finite two dimensional CW complex. By considering cohomology, we observe that…

We show that the spaces of holomorphic and continuous maps from a smooth complex projective variety to a projective space have the same homology in a range depending on the degree of the maps.

This paper aims to give some examples of diffeomorphic (or homeomorphic) low-dimensional complete intersections, which can be considered as a geometrical realization of classification theorems about complete intersections. A conjecture of…

In this paper we study the actions of tori (standard compact tori, as well as their quaternionic analogues) on products of spheres. It is proved that the orbit space of a specific action of a torus on a product of spheres is homeomorphic to…

We study asymptotic topological regularity of CAT(0) spaces. We prove that if a purely n-dimensional, proper, geodesically complete CAT(0) space has small volume growth, then it is homeomorphic to the n-dimensional Euclidean space. We also…

We investigate to what extend finite-dimensional homogeneous locally compact $ANR$-spaces have common properties with Euclidean manifolds. Specially, the local structure of homogeneous $ANR$-spaces is described. Using that description, we…

We prove a structure theorem for ergodic homological rotation sets of homeomorphisms isotopic to the identity on a closed orientable hyperbolic surface: this set is made of a finite number of pieces that are either one-dimensional or almost…