Related papers: Digital $n-$Manifolds With Or Without Boundaries
Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…
We analyse the massless wave equation on a class of two dimensional manifolds consisting of an arbitrary number of topological cylinders connected to one or more topological spheres. Such manifolds are endowed with a degenerate…
We consider spaces for which there is a notion of harmonicity for complex valued functions defined on them. For instance, this is the case of Riemannian manifolds on one hand, and (metric) graphs on the other hand. We observe that it is…
This paper deals with the subject of infinitesimal variations of Euclidean submanifolds with arbitrary dimension and codimension. The main goal is to establish a Fundamental theorem for these geometric objects. Similar to the theory of…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
The field of multiple view geometry has seen tremendous progress in reconstruction and calibration due to methods for extracting reliable point features and key developments in projective geometry. Point features, however, are not available…
We give a generalization of Thurston's Bounded Image Theorem for skinning maps, which applies to pared 3-manifolds with incompressible boundary that are not necessarily acylindrical. Along the way we study properties of divergent sequences…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
The topic of fixed points in digital metric spaces has drawn yet more publications with assertions that are incorrect, incorrectly proven, trivial, or incoherently stated. We discuss publications with bad assertions concerning fixed points…
For non-compact manifolds with boundary we prove that bounded geometry defined by coordinate-free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geodesic coordinates. We produce a nice atlas…
This thesis represents the first step in an investigation of an interesting class of manifold-theoretic invariants of $E_n$-algebras which generalize topological Hochschild homology. The main goal of this thesis is to give a definition of…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are…
Existing computer vision systems can compete with humans in understanding the visible parts of objects, but still fall far short of humans when it comes to depicting the invisible parts of partially occluded objects. Image amodal completion…
We discuss the problem of finding an analogue of the concept of a topological space in supergeometry, motivated by a search for a procedure to compactify a supermanifold along odd coordinates. In particular, we examine the topologies…
In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results…
This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image space are used to parameterize image filters which are used…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
Point clouds are popular 3D representations for real-life objects (such as in LiDAR and Kinect) due to their detailed and compact representation of surface-based geometry. Recent approaches characterise the geometry of point clouds by…
We introduce new topological quantum invariants of compact oriented 3-manifolds with boundary where the boundary is a disjoint union of two identical surfaces. The invariants are constructed via surgery on manifolds of the form $F \times I$…