arXiv research

Clusters on simple manifolds have connected boundaries.

The paper studies complexes of hypersurfaces in homology classes and proves their connectedness and simple connectedness.

The boundary of hyperbolic groups is locally simply connected.

We analyze total, asymmetric and frequency connectedness between oil and forex markets using high-frequency, intra-day data over the period 2007 -- 2017. By employing variance decompositions and their spectral representation in combination with realized semivariances to account for asymmetric and frequency connectednes…

We show that the Basilica Thompson group introduced by Belk and Forrest is not finitely presented, and in fact is not of type FP_2. The proof involves developing techniques for proving non-simple connectedness of certain subcomplexes of CAT(0) cube complexes.

Geodesic connectedness proved for statistical manifolds with divisible cubic forms.

Retrospective and prospective analysis of Diebold-Yilmaz connectedness research.

We propose a new framework for measuring connectedness among financial variables that arises due to heterogeneous frequency responses to shocks. To estimate connectedness in short-, medium-, and long-term financial cycles, we introduce a framework based on the spectral representation of variance decompositions. In an e…

Study examines grain futures connectedness during Russia-Ukraine conflict.

Let $X$ be a non-collapsing Ricci limit space and let $x\in X$. We show that for any $ε>0$, there is $r>0$ such that every loop in $B_t(x)$ is contractible in $B_{(1+ε)t}(x)$, where $t\in(0,r]$. In particular, $X$ is semi-locally simply connected.

The paper connects curvature positivity to rational connectedness in complex geometry.

We provide an easily verifiable condition for local $k$-connectedness of an inverse limit of polyhedra.

Study shows connectedness of Bowditch boundary persists in long Dehn fillings.

This paper develops a new portfolio optimization framework that considers network spillovers.

Connectedness proved for $\mathbb{Z}^d$ actions on 1D manifolds by $C^2$ diffeomorphisms.

New conditions ensure geodesic connectedness of affine manifolds.

In this paper we prove the path connectedness of the moduli spaces of metrics with positive isotropic curvature on certain compact four-dimensional manifolds.

This study analyzes dynamic connectedness in global supply chain infrastructure portfolios, identifying key risk factors and extreme events.

We study the connectedness of the planar self-affine sets $T(A,{\mathcal{D}})$ generated by an integer expanding matrix $A$ with $|\det(A)|=3$ and a non-collinear digit set ${\mathcal D}=\{0, v, kAv\}$ where $k\in {\mathbb Z}\setminus\{0\}$ and $v\in {\mathbb Z}^2$ such that $\{v, Av\}$ is linearly independent. By chec…

Connectedness of small clusters in Riemannian and Finsler manifolds proven.

Work consists of introduction, two chapters, conclusion and four applications. In this work is examined the condition, with which the wave space metrics of Riemann- Cartan is the solution of Einstein equation in the void. Geometric structures were for this purpose studied on the differentiated variety: connectedness, c…

In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly we prove the orbifold versions of the abelian connectedness and convexity theorems. In the second half, we prove that compact symplectic orbifolds with completely integrable torus acti…

Graph conditions ensure matching arc complexes are connected and hyperbolic.

Develops a new framework to measure network connectedness across and within markets.

A motif-based framework identifies local spillover structures in financial markets.

New proof shows path-connectedness of actions on intervals and circles.

A new technique for the study of geodesic connectedness in a class of Lorentzian manifolds is introduced. It is based on arguments of Brouwer's topological degree for the solution of functional equations. It is shown to be very useful for multiwarped spacetimes, which include different types of relativistic spacetimes.

Study on systemic risk in European insurance sector, showing insurer connections during stress.

In the paper, we focus on the connectedness of planar self-affine sets $T(A,{\mathcal{D}})$ generated by an integer expanding matrix $A$ with $|\det (A)|=3$ and a collinear digit set ${\mathcal{D}}=\{0,1,b\}v$, where $b>1$ and $v\in {\mathbb{R}}^2$ such that $\{v, Av\}$ is linearly independent. We discuss the domain of…

In this paper we extend the results of Kirwan et alii on convexity properties of the moment map for Hamiltonian group actions, and on the connectedness of the fibers of the moment map, to the case of non-compact orbifolds. Our motivation is twofold. First, the category of orbifolds is important in symplectic geometry b…

This paper explores the relation between convex functions and the geometry of space-times and semi-Riemannian manifolds (an investigation initiated by Gibbons-Ishibashi). Specifically, we study geodesic connectedness. We give geometric-topological proofs of geodesic connectedness for classes of space-times to which kno…

The paper proves rational connectedness for certain Kähler manifolds.

In this note we reduce the problem of geodesic connectedness in a wide class of Gödel type spacetimes to the search of critical points of a functional naturally involved in the study of geodesics in standard static spacetimes. Then, by using some known accurate results on the latter, we improve previous results on the …

The main goal of the paper is to prove the existence of the universal cover for $RCD^*(K,N)$-spaces. This generalizes earlier work of C. Sormani and the second named author on the existence of universal covers for Ricci limit spaces. As a result, we also obtain several structure results on the (revised) fundamental gro…

Asymmetries in volatility spillovers are highly relevant to risk valuation and portfolio diversification strategies in financial markets. Yet, the large literature studying information transmission mechanisms ignores the fact that bad and good volatility may spill over at different magnitudes. This paper fills this gap…

We review geometrical properties of a static spacetime $(M,g)$, including geodesic completeness, causality, standard splittings, compact $M$, closed geodesics and geodesic connectedness. We pay special attention to the critical quadratic behavior at infinity of the coefficients $β$, $β^{-1}$ ($β= -g(K,K)$, being $K$ a …

For a boundary-reducible $3$-manifold $M$ with $\partial M$ a genus $g$ surface, we show that if $M$ admits a genus $g+1$ Heegaard surface $S$, then the disk complex of $S$ is simply connected. Also we consider the connectedness of the complex of reducing spheres. We investigate the intersection of two reducing spheres…

Study introduces indecomposability for varifolds, leading to geometric consequences.

New model predicts financial connectedness via COVID-19 spread.

New algebra models refine complex manifold homotopy groups.

We report on time-varying network connectedness within three banking systems: North America, the EU, and ASEAN. The original method by Diebold and Yilmaz is improved by using exponentially weighted daily returns and ridge regularization on vector autoregression (VAR) and forecast error variance decomposition (FEVD). We…

We study a regular closure operator in the category of quandles. We show that the regular closure operator and the pullback closure operator corresponding to the reflector from the category of quandles to its full subcategory of trivial quandles coincide, we give a simple description of this closure operator, and analy…

Homotopy connectedness theorems for complex submanifolds of homogeneous spaces (sometimes referred to as theorems of Barth-Lefshetz type) have been established by a number of authors. Morse Theory on the space of paths lead to an elegant proof of homotopy connectedness theorems for complex submanifolds of Hermitian sym…

Study examines dynamic relationship between BRICS stocks and cryptocurrencies.

Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and available data. Often it is desirable to learn sparse graphs. However, making a grap…

This paper introduces forward-looking measures of the network connectedness of fears in the financial system, arising due to the good and bad beliefs of market participants about uncertainty that spreads unequally across a network of banks. We argue that this asymmetric network structure extracted from call and put tra…

In this paper, we determine the group of contact transformations modulo contact isotopies for Legendrian circle bundles over closed surfaces of nonpositive Euler characteristic. These results extend and correct those presented by the first author in a former work. The main ingredient we use is connectedness of certain …

In this paper, we consider the connectedness of planar self-affine set $T(A,\mathcal{D})$ arising from an integral expanding matrix $A$ with characteristic polynomial $f(x)=x^2+bx+c$ and a digit set $\mathcal{D}=\{0,1,\dots, m\}v$. The necessary and sufficient conditions only depending on $b,c,m$ are given for the $T(A…