相关论文: The topology and geometry of contact structures in…

These notes are an expanded version of an introductory lecture on contact geometry given at the 2001 Georgia Topology Conference. They are intended to present some of the "topological" aspects of three dimensional contact geometry.

Using contact homology, we reobtain some recent results of Geiges and Gonzalo about the fundamental group of the space of contact structures on some 3-manifolds. We show that our techniques can be used to study higher dimensional contact…

In this note we briefly review some recent results of the authors on the topological and geometrical properties of 3-cosymplectic manifolds.

The main purpose of this article is to classify contact structures on some 3-manifolds, namely lens spaces, most torus bundles over a circle, the solid torus, and the thickened torus T^2 x [0,1]. This classification completes earlier work…

Determining the associated metrics we get a local classification of contact metric three manifolds.

We survey what is known about various special types of submanifolds of contact manifolds and discuss their role in the development of contact geometry.

This expository paper explores the interaction of group ordering with topological questions, especially in dimensions 2 and 3. Among the topics considered are surfaces, braid groups, 3-manifolds and their structures such as foliations and…

We generalise the notion of contact manifold by allowing the contact distribution to have codimension two. There are special features in dimension six. In particular, we show that the complex structure on a three-dimensional complex contact…

These are lecture notes on cut-and-paste methods in 3-dimensional contact geometry.

Contact Geometry is an odd dimensional analogue of Symplectic Geometry. This vague idea can actually be formalized in a rather precise way by means of a Symplectic-to-Contact Dictionary. The aim of this review paper is discussing the basic…

We study low-dimensional problems in topology and geometry via a study of contact and Cauchy-Riemann ($CR$) structures. A contact structure is called spherical if it admits a compatible spherical $CR$ structure. We will talk about spherical…

This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.

This is an introductory text on the more topological aspects of contact geometry, written for the Handbook of Differential Geometry vol. 2. After discussing (and proving) some of the fundamental results of contact topology (neighbourhood…

This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.

In this note we study contact structures on 5-dimensional manifolds. We give a complete answer under the assumption that the Abundance conjecture holds in dimension 5.

This is a survey article on the recent development of "stringy geometry and topology of orbifolds", a new subject of mathematics motivated by orbifold string theory.

Twists of contact structures in dimension 3 and higher are studied in this paper from a viewpoint of contact round surgery. Three kinds of new modifications of contact structures which are higher-dimensional generalizations of the…

The purpose of this paper is to construct topology on vague soft sets. The concept of vague soft topology is introduced and its basic properties are given.

Some basic geometric properties related to connectedness and topological dimension 0 are discussed, especially in connection with the ultrametric version of the triangle inequality.

We define a graph encoding the structure of contact surgery on contact 3-manifolds and analyze its basic properties and some of its interesting subgraphs.