相关论文: Contact geometry
We investigate the local geometry of a pair of independent contact structures on 3-manifolds under maps that independently preserve each contact structure. We discover that such maps are homotheties on the contact 1-forms and we discover…
This is the first chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.
In this survey, we give an overview of Brieskorn manifolds and varieties, and their role in contact topology. We discuss open books, fillings and invariants such as contact and symplectic homology. We also present some new results involving…
We give an introduction to the physics and mathematics involved in the recently observed relation between topological string theory and knot contact homology and then discuss this relation. The note is based on two lectures given at the…
As shown by H. Gluck in 1962, the diffeotopy group of S^1 \times S^2 is isomorphic to Z_2 + Z_2 + Z_2. Here an alternative proof of this result is given, relying on contact topology. We then discuss two applications to contact topology: (i)…
We study generalized almost contact structures on odd-dimensional manifolds. We introduce a notion of integrability and show that the class of these structures is closed under symmetries of the Courant-Dorfman bracket, including T-duality.…
This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.
We give detailed exposition of modern differential geometry from global coordinate independent point of view as well as local coordinate description suited for actual computations. In introduction, we consider Euclidean spaces and different…
We prove that for regular contact forms there exists a bijective correspondence between the $C^0$ limits of sequences of smooth strictly contact isotopies and the limits with respect to the contact distance of their corresponding…
The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…
This is the third installment in a series of papers on the subject of derived contact structures. In this paper, we formally introduce the notion of a Legendrian structure in the derived context and provide natural constructions. We then…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
In discrete geometry, the contact number of a given finite number of non-overlapping spheres was introduced as a generalization of Newton's kissing number. This notion has not only led to interesting mathematics, but has also found…
The Whitney-Graustein theorem states that regular closed curves in the 2-plane are classified, up to regular homotopy, by their rotation number. Here we give a simple proof based on contact geometry.
The theory of $G$-structures provides us with a unified framework for a large class of geometric structures, including symplectic, complex and Riemannian structures, as well as foliations and many others. Surprisingly, contact geometry -…
The main subject of the book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in differential geometry. The book can be used as a reference manual, review of the existing results and introduction to some…
For contact manifolds, it is well-known that the map which assigns to an infinitesimal contact transformation its contact Hamiltonian function is a linear isomorphism, and an explicit local formula for its inverse can be given. In contrast,…
In these notes we discuss Lorentz-Finsler metrics, a notion originated in relativity theory, on certain groups of symplectic and contact transformations. Some basic geometric questions arising in this context concerning distance, geodesics…
We characterise the quotient surface graphs arising from symmetric contact systems of line segments in the plane and also from symmetric pointed pseudotriangulations in the case where the group of symmetries is generated by a translation or…
We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e.,…