相关论文: Lectures on open book decompositions and contact s…

Closed (and simply-connected) manifolds whose dimensions are larger than 4 are central geometric objects in classical algebraic topology and differential topology. They have been classified via algebraic and abstract objects. On the other…

In this note we observe, answering a question of Eliashberg and Thurston, that all contact structures on a closed oriented 3-manifold are $C^\infty$-deformations of foliations.

In this note we introduce the (homologically essential) arc complex of a surface as a tool for studying properties of open book decompositions and contact structures. After characterizing destabilizability in terms of the essential…

The present lectures were prepared for the Faro International Summer School on Factorization and Integrable Systems in September 2000. They were intended for participants with the background in Analysis and Operator Theory but without…

Two constructions of contact manifolds are presented: (i) products of S^1 with manifolds admitting a suitable decomposition into two exact symplectic pieces and (ii) fibre connected sums along isotropic circles. Baykur has found a…

In this paper, we study contact structures on any open 3-manifold V which is the interior of a compact 3-manifold. To do this, we introduce proper contact isotopy invariants called the slope at infinity and the division number at infinity.…

This is a survey of contact homology and its applications to the study of contact manifolds. It is a small tribute to Yasha Eliashberg's huge generosity with his countless explanations of his deep mathematical insights all along his career.…

These are notes from an informal mini-course on factorization homology, infinity-categories, and topological field theories. The target audience was imagined to be graduate students who are not homotopy theorists.

We give an introduction to the structure theory of extended affine Lie algebras, which provide a common framework for finite-dimensional semisimple, affine and toroidal Lie algebras. The notes are based on a lecture series given during the…

This survey is based on a series of five lectures, given May 3--7, 2010, at the Centre de Recerca Matematica, Barcelona. The goal of the lectures was to present aspects of the theory of foliation dynamical systems which have particular…

We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class…

These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

In this second paper of a two-part series, we prove that whenever a contact 3-manifold admits a uniform spinal open book decomposition with planar pages, its (weak, strong and/or exact) symplectic and Stein fillings can be classified up to…

These notes give an introduction to embedded contact homology (ECH) of contact three-manifolds, gathering together many basic notions which are scattered across a number of papers. We also discuss the origins of ECH, including various…

Let M be a closed oriented 3-manifold such that S^1 x M admits a symplectic structure w. The goal of this paper is to show that M is a fiber bundle over S^1. The basic idea is to use the obvious S^1-action on S^1 x M by rotating the first…

In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian to Hamiltonian classical field theories, and then we…

In this paper, we survey recent works on the structure of the mapping class groups of surfaces mainly from the point of view of topology. We then discuss several possible directions for future research. These include the relation between…

The aim of this article is to give practicing teachers an overview about the theory behind paperfolding, it is my qualifying thesis(Zulassungsarbeit) as a teacher in Germany. It is a survey about the relations between paperfolding and…

Classical contact Lie algebras are the fundamental algebraic structures on the manifolds of contact elements of configuration spaces in classical mechanics. In this paper, we determine the structure of the currently largest known category…