Related papers: Topological Lensing in Spherical Spaces
The abundance of peaks in weak gravitational lensing maps is a potentially powerful cosmological tool, complementary to measurements of the shear power spectrum. We study peaks detected directly in shear maps, rather than convergence maps,…
Recent observations suggest that the ratio of the total density to the critical density of the universe, $\Omega_0$, is likely to be very close to one, with a significant proportion of this energy being in the form of a dark component with…
If the Universe satisfies a perturbed Friedmann-Lema\^{\i}tre model, then the bright matter (e.g. radio-loud active galactic nuclei, RLAGNs) may be topologically lensed by global geometry. The generation of candidate topological lensing…
Collider events with multi-stage cascade decays fill out the kinematically allowed region in phase space with a density that is enhanced at the boundary. The boundary encodes all available information about the spectrum and is well…
The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such…
We investigate the formation of trapped surfaces in cosmological spacetimes, using constant mean curvature slicing. Quantitative criteria for the formation of trapped surfaces demonstrate that cosmological regions enclosed by trapped…
Tiny fluctuations of the Cosmic Microwave Background as well as various observable quantities obtained by spin raising and spin lowering of the effective gravitational lensing potential of distant galaxies and galaxy clusters, are described…
Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical {\em ansatz}, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
We find the complete rational homology for the finite subset spaces of a $d$-dimensional sphere. We also determine the integral homology in top $d$ degrees and obtain a partial description of it in codimension $d$.
We present a method to search for large angular-scale correlations, termed topological signatures, in the angular distribution of cosmic objects, which does not depend on cosmological models or parameters and is based only on the angular…
If the universe is finite and smaller than the distance to the surface of last scatter, then the signature of the topology of the universe is writ large on the microwave background sky. We show that the microwave background will be…
A new, improved version of a cosmic crystallography method for constraining cosmic topology is introduced. Like the circles-in-the-sky method using CMB data, we work in a thin, shell-like region containing plenty of objects. Two pairs of…
Observations of microwave background fluctuations can yield information not only about the geometry of the universe, but potentially about the topology of the universe. If the universe is negatively curved, then the characteristic scale for…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
Galaxy superclusters, the largest galaxy structures in the cosmic web, are formed due to the gravitational collapse (although they are not usually gravitationally bound). Their geometrical properties can shed light on the structure…
In this paper we present an implementation of a computer algorithm that automatically determines the topological structure of spacetime, using a branched covering space representation. This algorithm is applied to a few simple examples in…
In this article we propose an original classification method for unobscured imaging systems unfolded in two dimensions. This classification is based on a study of off-axis properties, and relies on topology and algorithm of real algebraic…
Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…
We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Buesemann, our concept also applies to metric spaces that might…