Related papers: Contiguity Distance between Simplicial Maps
Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under…
In this paper, we consider holomorphic mappings between real hypersurfaces in different dimensional complex spaces. We give a number of conditions that imply that such mappings are transversal to the target hypersurface at most points.
The present article deals with properties of one map between two expansions of real numbers of the Salem type. Differential, integral, and other properties of the function were considered.
We determine the symmetrized topological complexity of the circle, using primarily just general topology.
In this paper we analyze some relationships between the topological complexity of a space $X$ and the category of $C_{\Delta_X},$ the homotopy cofibre of the diagonal map $\Delta_X:X\rightarrow X\times X.$ We establish the equality of the…
We introduce a natural notion of holomorphic map between generalized complex manifolds and we prove some related results on Dirac structures and generalized Kaehler manifolds.
The homology groups of a simplicial complex reveal fundamental properties of the topology of the data or the system and the notion of topological stability naturally poses an important yet not fully investigated question. In the current…
We introduce the notion of filtration between topologies and study its stabilization properties. Descriptive set theoretic complexity plays a role in this study. Filtrations lead to natural transfinite sequences approximating a given…
In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…
We show that every continuous map from one translationally finite tiling space to another can be approximated by a local map. If two local maps are homotopic, then the homotopy can be chosen so that every interpolating map is also local.
We study properties of shy maps in digital topology.
We study the homotopy types of spaces of algebraic (rational) maps from real projective spaces into complex projective spaces. In a previous paper we have shown that the inclusion of the first space into the second one is a homotopy…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
Intersection homology is obtained from ordinary homology by imposing conditions on how the embedded simplices meet the strata of a space $X$. In this way, for the middle perversity, properties such as strong Lefschetz are preserved. This…
We study metrics on two-dimensional simplicial complexes that are conformal either to flat Euclidean metrics or to the ideal hyperbolic metrics described by Charitos and Papadopoulos. Extending the results of our previous paper, we prove…
For a simplicial manifold we construct the differential geometry structure and use it to investigate linear connections, metric and gravity. We discuss and compare three main approaches and calculate the resulting gravity action…
Motivated by the Lipschitz rigidity problem in scalar curvature geometry, we prove that if a closed smooth spin manifold admits a distance decreasing continuous map of non-zero degree to a sphere, then either the scalar curvature is…
Distance geometry is the study of the arrangements of points in space using only the mutual distances between them. The basic idea in this letter is to use distance geometry for thermodynamics studies of small clusters in the microcanonical…
We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…
The interrelations between various classes of convergence spaces defined by countability conditions are studied. Remarkably, they all find characterizations in the usual space of ultrafilters in terms of classical topological properties.…