Related papers: The topology and geometry of contact structures in…
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…
A book, concerning the classical restricted three body problem, and the approach to this old conundrum coming from the modern methods of symplectic and contact geometry. It is split into Part I (theoretical aspects), and Part II (practical…
We outline the basic ideas of the topological mechanisms of superconductivity. A gauged model of correlated electronic system where a topological fluid is formed as a result of a strong interaction is discussed.
In the paper we prove, that extrinsic curvature does not impose restrictions on the topology of a contact structure, except the obvious ones.
This survey aims to give an overview of several substantial developments of the last 50 years in the structure theory of regular semigroups and to shed light on their impact on other parts of semigroup theory.
Many different and complementary strategies for translating the basic principle of multiple topological imaging into observational analysis are now available, both for three-dimensional and two-dimensional catalogues.
The goal of this survey is to give a list of resent results about topology of manifolds admitting different metrics with the same geodesics. We emphasize the role of the theory of integrable systems in obtaining these results.
We present a simple visual description of the topology of the space of three-dimensional rotations, requiring just intuition, imagination and no advanced math.
This paper aims to provide a careful and self-contained introduction to the theory of topological degree in Euclidean spaces. It is intended for people mostly interested in analysis and, in general, a heavy background in algebraic or…
This paper begins the study of relations between Riemannian geometry and contact topology in any dimension and continues this study in dimension 3. Specifically we provide a lower bound for the radius of a geodesic ball in a contact…
Wettability of a surface depends on both surface chemistry and topography. To move a three-phase contact line, a de-pinning force needs to be applied, which is of practical importance in various applications. However, a unified…
In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of the intrinsic geometry is given. A new type of…
We show the equivalence of several notions in the theory of taut foliations and the theory of tight contact structures. We prove equivalence, in certain cases, of existence of tight contact structures and taut foliations.
We extend the notions of complete intersection dimension and lower complete intersection dimension to the category of complexes with finite homology and verify basic properties analogous to those holding for modules. We also discuss the…
We review some aspects of theories with compact extra dimensions. We consider the motivation and the theoretical basis of Large, Universal and Warped Extra Dimensions. We focus on those aspects that are potentially relevant in the…
An overview of the current data and phenomenology on the structure of the photon and an outline of some opportunities available in the medium term future.
We propose a measure of shape which is appropriate for the study of a complicated geometric structure, defined using the topology of neighborhoods of the structure. One aspect of this measure gives a new notion of fractal dimension. We…
This survey is an invitation to recent developments in higher dimensional birational geometry.
We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.
In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.