相关论文: Moment-angle manifolds associated to neighbourly t…

The trace of $n$-framed surgery on a knot in $S^3$ is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded 2-sphere…

Often noisy point clouds are given as an approximation of a particular compact set of interest. A finite point cloud is a compact set. This paper proves a reconstruction theorem which gives a sufficient condition, as a bound on the…

We prove a "gluing" theorem for monotone homotopies; a monotone homotopy is a homotopy through simple contractible closed curves which themselves are pairwise disjoint. We show that two monotone homotopies which have appropriate overlap can…

In this article we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras we study homotopes by methods of Category theory and give description of so-called well-tempered elements…

We study existence and non-existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all critical points of the Hilbert-Einstein functional…

Let $M$ be a non-compact hyperbolic $3$-manifold with finite volume and totally geodesic boundary components. By subdividing mixed ideal polyhedral decompositions of $M$, under some certain topological conditions, we prove that $M$ has an…

Here, an extension of the Obata-Tanno's theorem to Finsler geometry is established and the following rigidity result is obtained; Every complete connected Finsler manifold of positive constant flag curvature is isometrically homeomorphic to…

We consider an extremal problem for subsets of high-dimensional spheres that can be thought of as an extension of the classical isoperimetric problem on the sphere. Let $A$ be a subset of the $(m-1)$-dimensional sphere $\mathbb{S}^{m-1}$,…

The truncated multidimensional moment problem is studied in terms of the Stieltjes transform as the interpolation problem. A step-by-step algorithm is constructed for the multidimensional moment problem and the set of solutions is found in…

In the present paper we study hyperbolic manifolds that are rational homology 3-spheres obtained by colouring of right--angled polytopes. We study the existence (or absence) of different kinds of symmetries of rational homology spheres that…

The classical Minkowski formula is extended to spacelike codimension-two submanifolds in spacetimes which admit "hidden symmetry" from conformal Killing-Yano two-forms. As an application, we obtain an Alexandrov type theorem for spacelike…

Topological methods have emerged as valuable tools for analyzing the structural properties of directed graphs, particularly connectome data in computational neuroscience. This paper investigates the construction of topological spaces from…

The problem of splitting a homotopy equivalence along a submanifold is closely related to the surgery exact sequence and to the problem of surgery of manifold pairs. In classical surgery theory there exist two approaches to surgery in the…

Let $M$ be a smooth, orientable, closed, connected $4$-manifold and suppose that $H_1(M;\mathbb{Z})$ is finitely generated and has no $2$-torsion. We give a homotopy decomposition of the suspension of $M$ in terms of spheres, Moore spaces…

We define a model for the homology of manifolds and use it to describe the intersection product on the homology of compact oriented manifolds and to define homological quantum field theories which generalizes the notions of string topology…

Let $M$ be a closed $n$-manifold with nonzero simplicial volume. A central result in systolic geometry from Gromov is that systolic volume of $M$ is related to its simplicial volume. In this short note, we show that systolic volume of…

The work develops further the theory of the following inversion problem, which plays the central role in the rapidly developing area of thermoacoustic tomography and has intimate connections with PDEs and integral geometry: {\it Reconstruct…

Given a Lie group acting on a manifold $M$ preserving a closed $n+1$-form $\omega$, the notion of homotopy moment map for this action was introduced in Callies-Fregier-Rogers-Zambon [6], in terms of $L_{\infty}$-algebra morphisms. In this…

This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport's problem regarding badly approximable points on submanifolds of a Euclidean space and Schmidt's problem regarding the intersections of…

This paper is a survey of recent advances as well as open problems in the study of face numbers of centrally symmetric simplicial polytopes and spheres. The topics discussed range from neighborliness of centrally symmetric polytopes and the…