Related papers: Slant products on the Higson-Roe exact sequence

For any compact Hausdorff space $K$ we construct a canonical finitary coarse structure $\mathcal E_{X,K}$ on the set $X$ of isolated points of $K$. This construction has two properties: $\bullet$ If a finitary coarse space $(X,\mathcal E)$…

We combine our results on symmetric products and second quantization with our description of discrete torsion in order to explain the ring structure of the cohomology of the Hilbert scheme of points on a K3 surface. This is achieved in…

One primary objective in submanifold geometry is to discover fascinating and significant classical examples of $H_1$. In this paper which relies on the theory we established in [Adv. Math. 405 (2022), 08514, 50 pages, arXiv:2101.11780] and…

On a Riemannian almost product manifold $(M,P,g)$ we consider a linear connection preserving the almost product structure $P$ and the Riemannian metric $g$ and having a totally skew-symmetric torsion. We determine the class of the manifolds…

In this paper, we show the fundamental theorems for rotationally symmetric hypersurfaces, and thus, together with the earlier results in [3] and [4], provide a complete classification of umbilic hypersurfaces in the Heisenberg groups…

We consider Einstein hypersurfaces of warped products $I\times_\omega\mathbb Q_\epsilon^n,$ where $I\subset\mathbb R$ is an open interval and $\mathbb Q_\epsilon^n$ is the simply connected space form of dimension $n\ge 2$ and constant…

We develop an approach to calculating the cup and cap products on Hochschild cohomology and homology of curved algebras associated with polynomials and their finite abelian symmetry groups. For polynomials with isolated critical points, the…

In the paper we study the preservation of pseudocompactness (resp., countable compactness, sequential compactness, $\omega$-boundedness, totally countable compactness, countable pracompactness, sequential pseudocompactness) by Tychonoff…

Let $\mathbf{TB}$ be the category of totally bounded, locally compact metric spaces with the $C_0$ coarse structures. We show that if $X$ and $Y$ are in $\mathbf{TB}$ then $X$ and $Y$ are coarsely equivalent if and only if their Higson…

In this paper, we prove a dihedral extremality and rigidity theorem for a large class of codimension zero submanifolds with polyhedral boundary in warped product manifolds. We remark that the spaces considered in this paper are not…

We study stability properties of the Haagerup property and of coarse embeddability in a Hilbert space, under certain semidirect products. In particular, we prove that they are stable under taking standard wreath products. Our construction…

We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields $k$ of characteristic $0$ and…

We study the locus of smooth hypersurfaces inside the Hilbert scheme of a smooth projective complex variety. In the spirit of scanning, we construct a map to a continuous section space of a projective bundle, and show that it induces an…

We investigate generalisations of Hitchin's functionals, whose critical points correspond to nearly K\"ahler and nearly parallel $G_2$-structures. Our focus is on the gradient flow of these functionals and the spectral decomposition of…

Given a finite group G and a G-space X, we show that a direct sum $F_G (X) = \bigoplus_{n \geq 0}K_{G_n} (X^n) \bigotimes \C$ admits a natural graded Hopf algebra and $\lambda$-ring structure, where $G_n$ denotes the wreath product $G \sim…

The intent of this article is to study some special $n$-dimensional continua lying in products of $n$ curves. (The paper is an improved version of a portion of \cite{K-K-S}.) We show that if $X$ is a locally connected, so-called, quasi…

Let $\H$ denote the discrete Heisenberg group, equipped with a word metric $d_W$ associated to some finite symmetric generating set. We show that if $(X,\|\cdot\|)$ is a $p$-convex Banach space then for any Lipschitz function $f:\H\to X$…

In this paper, it is shown that every right $\omega$-narrow strongly topological gyrogroup $G$ is right $\omega$-balanced by applying the gyrosemidirect product groups. Then we investigate the class of $\sigma$-compact strongly topological…

Let $S \subset \mathbb{Z}^{d}$ be a finitely generated subsemigroup. Let $E$ be a product system over $S$. We show that there exists an infinite dimensional separable Hilbert space $\mathcal{H}$ and a semigroup $\alpha:=\{\alpha_x\}_{x \in…

We introduce smooth atlas stratified spaces. We show that this class is closed under cartesian products; consequently, it is possible to define fiber bundles of smooth atlas stratified spaces. We describe the resolution of such a space to a…