Related papers: Formal Barycenter Spaces with Weights: The Euler C…

Datasets are mathematical objects (e.g., point clouds, matrices, graphs, images, fields/functions) that have shape. This shape encodes important knowledge about the system under study. Topology is an area of mathematics that provides…

In the main result of the paper we extend Rosenthal's characterization of Banach spaces with the Schur property by showing that for a quasi-complete locally convex space $E$ whose separable bounded sets are metrizable the following…

We introduce noncommutative weak Orlicz spaces associated with a weight and study their properties. We also define noncommutative weak Orlicz-Hardy spaces and characterize their dual spaces.

It is shown that the Euler characteristic $\chi_{(\mathcal{H},\mathcal{B},\epsilon_q)}$ of a $\mathbb{Z}[[q]]$-Hecke algebra $\mathcal{H}$ associated with a finitely generated Coxeter group $(W,S)$ coincides with $p_{(W,S)}(q)^{-1}$, where…

This study proposes a novel approach to extract topological properties, specifically the Euler characteristic, from input images using neural networks without relying on large pre-existing datasets but with a single geometric image.…

We use some basic properties of binomial and Stirling numbers to prove that the Euler characteristic is, essentially, the unique numerical topological invariant for compact polyhedra which can be expressed as a linear combination of the…

In this paper we discuss compactness estimates for the $\bar \partial $-Neumann problem in the setting of weighted $L^2$-spaces on $\mathbb{C}^n.$ For this purpose we use a version of the Rellich - Lemma for weighted Sobolev spaces.

We prove that a locally nilpotent group $G$ of $C^{1}$ diffeomorphisms of a compact surface $S$ of non-vanishing Euler characteristic has a finite orbit ${\mathcal O}$ whose cardinal is bounded by above by a function of the characteristic…

In this paper we obtain some explicit expressions for the Euler characteristic of a rank n coherent sheaf F on P^N and of its twists F(t) as polynomials in the Chern classes c_i(F), also giving algorithms for the computation. The employed…

Let $a$ be a real number satisfying $0<a<\pi$. We denote by $M_n(a)$ the configuration space of regular spherical $n$-gons with side-lengths $a$. The purpose of this paper is to determine $\chi (M_n(a))$ for all $a$ and odd $n$. To do so,…

Indices of singular points of a vector field or of a 1-form on a smooth manifold are closely related with the Euler characteristic through the classical Poincar\'e--Hopf theorem. Generalized Euler characteristics (additive topological…

In this paper, we prove that a compact set $K\subset \mathbb{C}^n$ is the support of a weighted equilibrium measure if and only it is not pluripolar at each of its points extending a result of Saff and Totik to higher dimensions. Thus, we…

Manifolds admitting positive sectional curvature are conjectured to have rigid homotopical structure and, in particular, comparatively small Euler charateristics. In this article, we obtain upper bounds for the Euler characteristic of a…

We review different properties related to the Cauchy problem for the (nonlinear) Schrodinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in…

In this short note, we provide a calculation of the Euler characteristic of a finite homotopy colimit of finite cell complexes, which depends only on the Euler characteristics of each space and resembles Mobius inversion. Versions of the…

A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are…

We associate a rational number $\chi(\mathcal{A})$ to every category $\mathcal{A}$ whose object and morphism sets are finite. We show that the assignment $\chi$ is additive under disjoint union and it preserves products. Hence we consider…

Using a covariant description of the geometry of deformations for extendons, it is shown that the topological corrections for the string action associated with the Euler characteristic and the first Chern number of the normal bundle of the…

The index theorem of Euler-Poincar\'e characteristic of manifold with boundary is given by making use of the general decomposition theory of spin connection. We shows the sum of the total index of a vector field $\phi $ and half the total…

This paper is devoted to the study of a problem arising from a geometric context, namely the conformal deformation of a Riemannian metric to a scalar flat one having constant mean curvature on the boundary. By means of blow-up analysis…