Related papers: Lattices in hyperbolic buildings
Hyperbolic lattices are a new type of synthetic quantum matter emulated in circuit quantum electrodynamics and electric-circuit networks, where particles coherently hop on a discrete tessellation of two-dimensional negatively curved space.…
We define and study an extended hyperbolic space which contains the hyperbolic space and de Sitter space as subspaces and which is obtained as an analytic continuation of the hyperbolic space. The construction of the extended space gives…
We introduce the concept of basis for a lattice. This basis plays a vital role to determine the completeness and consistency of the lattice. Weighted lattices are introduced and its complexity is formulated. Some axiomatic systems,…
Some topics from recent progresses in lattice QCD are reviewed.
This is a very short introduction to hierarchically hyperbolic spaces and groups. It is aimed at non-experts, including anyone who may encounter a group with some similarities to mapping class groups.
The aim of this note is to present a construction of symplectic structures on orientable globally hyperbolic 4-dimensional lorentzian manifolds. Said structures are defined on the manifold itself, not on its cotangent bundle. It also…
We study convex subsets of buildings, discuss some structural features and derive several characterizations of buildings.
The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.
I discuss a new approach to constructing lattices for gauge theories with extended supersymmetry. The lattice theories themselves respect certain supersymmetries, which in many cases allows the target theory to be obtained in the continuum…
The combinatorial hierarchical hyperbolicity criterion is a very useful way of constructing new hierarchically hyperbolic spaces (HHSs). We show that, conversely, HHSs satisfying natural assumptions (satisfied, for example, by mapping class…
This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints were never completed. This eprint is only an…
We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…
This is an overview of the recent results of interaction of Boolean valued analysis and vector lattice theory.
We review recent results on congruence lattices of (infinite) lattices. We discuss results obtained with box products, as well as categorical, ring-theoretical, and topological results.
Sponges were recently proposed as a generalization of lattices, focussing on joins/meets of sets, while letting go of associativity/transitivity. In this work we provide tools for characterizing and constructing sponges on metric spaces and…
This article simply presents several coordinate systems for 2 and 3-dimensional hyperbolic spaces, describing the general solutions of Helmholtz equation in each one of these systems.
We give a short and purely bilinear proof of the fact that two chains of $p$-elementary lattices with quadratic form or alternating bilinear form over the $p$-adic integers ore more generally over a complete discrete valuation ring have…
In this paper, we study the intrinsic mean curvature flow on certain closed spacelike manifolds, and prove the existence of hyperbolic structures on them.
This is a brief and gentle introduction, aimed at graduate students, to the subject of model subspaces of the Hardy space.
The goal of this paper is to give a conjectural census of complex hyperbolic sporadic groups. We prove that only finitely many of these sporadic groups are lattices. We also give a conjectural list of all lattices among sporadic groups, and…