Related papers: Lattices in hyperbolic buildings
An introduction to Hyperbolic Analysis is presented.
We construct a nonuniform lattice and an infinite family of uniform lattices in the automorphism group of a hyperbolic building with all links a fixed finite building of rank 2 associated to a Chevalley group. We use complexes of groups and…
This is a short survey on finite-volume hyperbolic four-manifolds. We describe some general theorems and focus on the concrete examples that we found in the literature. The paper contains no new result.
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
An alternative method is described for determining the hyperbolic structure on a link complement, and some of its elementary consequences are examined. The method is particularly suited to alternating links.
The aim of this short lecture series is to expose the students to the beautiful theory of lattices by, on one hand, demonstrating various basic ideas that appear in this theory and, on the other hand, formulating some of the celebrated…
The aim of this short survey is to advertise various tools that have been developed to study hierarchically hyperbolic spaces (HHSs) in recent years, with particular emphasis on those that require little to no knowledge of the HHS machinery…
We discuss the notion of the universal relatively hyperbolic structure on a group which is used in order to characterize relatively hyperbolic structures on the group. We also study relations between relatively hyperbolic structures on a…
The first part of this survey is a heuristic, non-technical discussion of what an HHS is, and the aim is to provide a good mental picture both to those actively doing research on HHSs and to those who only seek a basic understanding out of…
The notions of mass and center of mass are extended to laminae of the hyperbolic plane. The resulting formulae contain many surprises.
This survey article describes the algorithmic approaches successfully used over the time to construct hyperbolic structures on 3-dimensional topological "objects" of various types, and to classify several classes of such objects using such…
A strong consequence of quadratic forms becoming hyperbolic over the function field of a form is established. This result is invoked to obtain a new characterisation of hyperbolicity over function fields, and to recover a number of…
In the hyperbolic plane there are infinite regular lattices. From a fix vertex of a lattice tree graphs can be constructed recursively to the next layers with edges of the lattice. In this article we examine the properties of the growing of…
This is a survey of characterizations and relationships between some properties of lattices, particularly the modular, Arguesian, linear, and distributive properties, but also some other related properties. The survey emphasizes finite and…
Signatures of superfluid-like behaviour have recently been observed experimentally in a nonlinear optical mesh lattice, where the arrival time of optical pulses propagating in a pair of coupled optical fiber loops is interpreted as a…
This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.
I give a brief introduction to lattice QCD for non-specialists.
This paper introduces a method of navigation in a large family of tilings of the hyperbolic plane and looks at the question of possible applications in the light of the few ones which were already obtained.
We present a basic introduction to the theories of M\"obius structures and hyperbolic ends and we study their applications to the theory of $k$-surfaces in $3$-dimensional hyperbolic space.
This is the author's PhD thesis, published at the Universit\"at M\"unster, Germany in 2010. It contains a detailed description of the results of arXiv:0903.1989, arXiv:0905.0071 and arXiv:0908.2713.