Related papers: Puzzles and Paradoxes About Holography
We introduce holed cone structures on 3-manifolds to generalize cone structures. In the same way as a cone structure, a holed cone structure induces the holonomy representation. We consider the deformation space consisting of the holed cone…
Within the framework of the "complexity equals action" and "complexity equals volume" conjectures, we study the properties of holographic complexity for rotating black holes. We focus on a class of odd-dimensional equal-spinning black holes…
This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into…
Holographic superconductor is an important arena for holography, as it allows concrete calculations to further understand the dictionary between bulk physics and boundary physics. An important quantity of recent interest is the holographic…
The Heesch problem 'grades' polygons that fail to tile the plane in terms of the number of layers (or corollas) of copies of it that can be formed around a central unit. We study the different topology of ' walls', which we define to be…
Some recent literature has examined the holographic-induced cosmology of a brane universe in the background of an anti-de Sitter-black hole geometry. In this regard, curved-brane scenarios have begun to receive considerable attention. Our…
A three-manifold equipped with a Heegaard diagram can be used to set up a Floer homology theory whose differential counts pseudo-holomorphic disks in the $g$-fold symmetric product of the Heegaard surface. This leads to a topological…
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs.
The Penrose triangle, staircase, and related ``impossible objects'' have long been understood as related to first cohomology $H^1$: the obstruction to extending locally consistent interpretations around a loop. This paper develops a…
Holographic displays promise to deliver unprecedented display capabilities in augmented reality applications, featuring a wide field of view, wide color gamut, spatial resolution, and depth cues all in a compact form factor. While emerging…
We provide a holographic interpretation of a class of three-dimensional wormhole spacetimes. These spacetimes have multiple asymptotic regions which are separated from each other by horizons. Each such region is isometric to the BTZ black…
Superoscillations can explain the arbitrarily high frequencies' paradox in black hole radiation
In this paper, we suggest a mathematical representation to the holographic principle through the theory topological retracts. We found that the topological retraction is the mathematical analogs of the hologram idea in modern quantum…
The notion of a holomorphically symplectic manifold can be generalized to the singular one. This paper studies the birational contraction maps between symplectic varieties, and then describes the deformation of a symplectic variety which…
Aspects of holography or dimensional reduction in gravitational physics are discussed with reference to black hole thermodynamics. Degrees of freedom living on Isolated Horizons (as a model for macroscopic, generic, eternal black hole…
This paper is removed from the network permanently. The content in this paper has now been put together with hep-th/9310183. See the recently replaced and widely revised version of the latter.
An odd hole in a graph is an induced subgraph which is a cycle of odd length at least five. In 1985, A. Gyarfas made the conjecture that for all t there exists n such that every graph with no K_t subgraph and no odd hole is n-colourable. We…
A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…
V.I. Arnold [Russian Math. Surveys 26(2) (1971) 29-43] constructed miniversal deformations of square complex matrices under similarity. Reduction transformations to them and also to miniversal deformations of matrix pencils and matrices…
Recently holographic prescriptions are proposed to compute quantum complexity of a given state in the boundary theory. A specific proposal known as `holographic subregion complexity' is supposed to calculate the the complexity of a reduced…