Non-collapsing Ricci limit spaces are shown to be semi-locally simply connected.
problem Understanding the topological properties of non-collapsing Ricci limit spaces.
method Demonstrated through the existence of a radius r for each point x in the space, such that loops are contractible within a larger radius. result Non-collapsing Ricci limit spaces are semi-locally simply connected.
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…
Extends foliation results to singular cases.
problem Understanding foliations near singular leaves.
method Proves semi-local Levi-Malcev theorem for holonomy Lie algebroid.
result Formal semi-local triviality for all 2-connected and a wide class of 1-connected leaves.
Study fundamental groups of RCD spaces without smoothness or curvature bounds.
problem Understanding fundamental groups of RCD spaces without additional conditions.
method Combining tools from RCD spaces, Gromov-Hausdorff convergence, and splitting theorems.
result Fundamental groups of RCD spaces are controlled by a finite number of generators and have specific properties under convergence.
Clusters on simple manifolds have connected boundaries.
problem Understanding the connectedness of boundaries of isoperimetric clusters.
method Analyzing isoperimetric clusters on simply connected homogeneous Riemannian manifolds.
result Clusters on such manifolds have connected boundaries.
Research shows RCD* spaces are semi-locally simply connected.
problem Understanding the topological properties of RCD* spaces.
method Proving semi-locally simply connected property for any point and radius.
result RCD* spaces are semi-locally simply connected.
Ricci limit spaces are semi-locally simply connected.
problem Understanding the topological properties of Ricci limit spaces.
method Demonstrating that for any loop in a specified radius, it can be contracted within a larger radius.
result Ricci limit spaces are semi-locally simply connected.
The paper studies complexes of hypersurfaces in homology classes and proves their connectedness and simple connectedness.
problem Investigating complexes of hypersurfaces in homology classes and proving their topological properties.
method Defining and analyzing simplicial complexes S†(M,φ) and T†(M,φ) for properly embedded hypersurfaces in n-manifolds, proving connectedness and simple connectedness. result Proves connectedness and simple connectedness of the complexes S†(M,φ) and T†(M,φ). We describe a semi-local canonical form for Legendrian foliations on contact manifolds in the neighbourhood of a Legendrian submanifold. This result generalizes local results by Libermann and Pang on Legendrian foliations on contact manifolds, and is analogeous to a semi-local result by Weinstein in the symplectic case…
The boundary of hyperbolic groups is locally simply connected.
problem Topology of hyperbolic group boundaries
method Proving local simple connectedness in terms of global topology
result Boundary is locally simply connected if and only if complement of any point is simply connected
We extend the cobordism based categorification of the virtual Jones polynomial to virtual tangles. This extension is combinatorial and has semi-local properties. We use the semi-local property to prove an applications, i.e. we give a discussion of Lee's degeneration of virtual homology.
A simple proof shows standard billiard for certain convex domains.
problem Characterizing billiards in convex domains that are both projective and Minkowski.
method Direct simple proof in C1-smoothness, semi-local and local versions proved. result Standard Euclidean billiard in an appropriate structure.
New Alexander invariants for knot groups computed using K1-groups.
problem Computing Alexander invariants for knot groups.
method Introducing K1-classes and comparing them with other Alexander polynomials. result Non-triviality of computed K1-classes for some knots. 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.
problem Geodesic connectedness of affine connections on statistical manifolds with divisible cubic forms.
method Analogy with Hopf-Rinow theorem in Riemannian geometry, establishing geodesic completeness.
result Geodesic connectedness established for statistical manifolds with divisible cubic forms.
We give a classification of generic bifurcations of intersections of wavefronts generated by different points of a hypersurface with or without boundaries.
Retrospective and prospective analysis of Diebold-Yilmaz connectedness research.
problem Assessing the Diebold-Yilmaz approach to dynamic network connectedness.
method Retrospective and prospective analysis of Diebold-Yilmaz (2014) and personal recollections.
result Personal insights and retrospective 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.
problem Quantile return connectedness of grain futures markets during geopolitical instability.
method Dynamic quantile VAR combined with frequency-domain decomposition.
result Heterogeneous spillovers across quantiles, with strong transmitters and persistent receivers.
Algorithm classifies saddle-focus singularities in Hamiltonian systems.
problem Classifying nondegenerate saddle-focus singularities in integrable Hamiltonian systems.
method Developed an algorithm based on semi-local equivalence to represent singularities as almost direct products.
result Obtained complete lists of saddle-focus singularities of complexities 1, 2, and 3.
The paper connects curvature positivity to rational connectedness in complex geometry.
problem Establishing a geometric criterion for rational connectedness.
method Uhlenbeck-Yau's continuity method applied to mean curvature positivity.
result Holomorphic tangent bundle mean curvature positivity is equivalent to rational connectedness of compact Kähler manifolds.
Symplectic classification for a specific type of singularity in integrable systems.
problem Symplectic classification of integrable systems near singular points of type An. method Real-analytic symplectic normal forms and classification of Lagrangian foliations.
result All integrable systems are symplectically equivalent near singular points of this type.
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.
problem Persistence of Bowditch boundary connectedness in Dehn fillings.
method Analysis of relatively hyperbolic group pairs and peripheral subgroups.
result Connectedness of Bowditch boundary persists in sufficiently long Dehn fillings without needing restrictions.
This paper develops a new portfolio optimization framework that considers network spillovers.
problem Modern financial markets' complex interconnections are not fully captured by variance alone.
method Formulates a three-objective optimization problem with a quadratic measure of network spillovers.
result Establishes a three-dimensional efficient surface and a risk-risk frontier.
Connectedness proved for Zd actions on 1D manifolds by C2 diffeomorphisms.
problem Connectedness of Zd actions by C2 diffeomorphisms on 1D manifolds. method Proved connectedness through continuous paths of C1+ac diffeomorphisms. result Connectedness of Zd actions by C2 diffeomorphisms on 1D manifolds. New conditions ensure geodesic connectedness of affine manifolds.
problem Ensuring geodesic connectedness in affine manifolds.
method New sufficient conditions for geodesic connectedness, weaker than previous work.
result Elementary proof of geodesic connectedness.
In this paper we prove the path connectedness of the moduli spaces of metrics with positive isotropic curvature on certain compact four-dimensional manifolds.
We extend Bar-Natan's cobordism based categorification of the Jones polynomial to virtual links. Our topological complex allows a direct extension of the classical Khovanov complex (h=t=0), the variant of Lee (h=0,t=1) and other classical link homologies. We show that our construction allows, over rings of characte…
This study analyzes dynamic connectedness in global supply chain infrastructure portfolios, identifying key risk factors and extreme events.
problem Understanding dynamic connectedness in global supply chain infrastructure portfolios under various risk factors and extreme events.
method Time-varying parameter vector autoregression (TVP-VAR) model to study spillover and interconnectedness of risk factors.
result Risk shocks influence dynamic connectedness between portfolios and risk factors, and extreme events affect investment outcomes.
We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed two families of plane curves with second order contact at the envelope.
We study the connectedness of the planar self-affine sets T(A,D) generated by an integer expanding matrix A with ∣det(A)∣=3 and a non-collinear digit set D={0,v,kAv} where k∈Z∖{0} and v∈Z2 such that {v,Av} is linearly independent. By chec…
A game on diagrams switches crossing directions to achieve connectedness.
problem Achieving connectedness in diagrams through crossing switches.
method Players switch crossing directions on regions of a diagram to achieve connectedness.
result Connectedness can be achieved through strategic crossing switches.
Connectedness of small clusters in Riemannian and Finsler manifolds proven.
problem Understanding connectedness of small clusters in Riemannian and Finsler manifolds.
method Proved connectedness and small diameter properties for clusters of small volume in both manifolds.
result Clusters in Riemannian manifolds are connected and have small diameter; in Finsler manifolds, they are at most m connected components of small diameter.
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…
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…
Graph conditions ensure matching arc complexes are connected and hyperbolic.
problem Conditions for connectedness and hyperbolicity of matching arc complexes.
method Conditions on finite simplicial graphs guaranteeing connectedness and hyperbolicity of matching arc complexes.
result Conditions on finite simplicial graphs ensure connectedness and hyperbolicity of matching arc complexes.
Develops a new framework to measure network connectedness across and within markets.
problem Lack of flexible methods to measure network connectedness and its evolution.
method Allows network nodes to be connected in clusters, with shocks orthogonal across clusters and correlated within clusters.
result Demonstrates the effectiveness of the new framework in a detailed empirical analysis of equity markets.
A motif-based framework identifies local spillover structures in financial markets.
problem Aggregate risk spillovers obscure local interaction patterns in systemic risk.
method Develops a motif-based framework using multiscale backbones and colored motifs.
result Motif-based portfolios outperform traditional benchmarks on risk-adjusted returns.
Paper measures asymmetric fear network connectedness for risk prediction.
problem Predicting macroeconomic conditions and economic uncertainty.
method Forward-looking measures from bank option prices.
result Asymmetric network structure predicts economic conditions.
New proof shows path-connectedness of actions on intervals and circles.
problem Path-connectedness of C1+ac actions of Zd. method New proof using C1 diffeomorphisms with absolutely continuous derivative. result Path-connectedness of the space of actions.
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.
problem Understanding systemic risk connectedness in European insurance sector.
method Common connectedness framework applied to returns, volatility, value-at-risk, and expected shortfall.
result Insurers are a significant component of systemic risk connectedness, especially during stress episodes.
In the paper, we focus on the connectedness of planar self-affine sets T(A,D) generated by an integer expanding matrix A with ∣det(A)∣=3 and a collinear digit set D={0,1,b}v, where b>1 and v∈R2 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.
problem Rational connectedness of compact Kähler manifolds.
method Uniform weak RC-positivity of the tangent bundle.
result Compact Kähler manifolds with uniformly weakly RC-positive tangent bundles are projective and rationally connected.