Open AccessBook
An introduction to contact topology
Hansjörg Geiges
- 01 Jan 2008
TL;DR: A comprehensive introduction to contact topology is given in this article, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds.
read more
Abstract: This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Lorentzian distance functions in contact geometry
08 Mar 2022
TL;DR: In this article , the authors define a class of Lorentzian distance functions on the group of contactomorphisms of a closed contact manifold depending on the choice of a contact form, and show that intervals defined by the positivity relation are open with respect to the topology induced by the Hofer norm.
•Posted Content
Legendrian contact homology in $\mathbb{R}^3$
John B. Etnyre,Lenhard Ng +1 more
TL;DR: In this paper, an introduction to Legendrian contact homology and the Chekanov-Eliashberg differential graded algebra is given, with a focus on the setting of Legendrian knots in $\mathbb{R}^3$.
On open book embedding of contact manifolds in the standard contact sphere
TL;DR: In this article, it was shown that a large class of contact 3-manifolds admit contact open book embedding in the standard contact 5-sphere, and that all Ustilovsky (4m + 1)-spheres contact open-book embeddings in the 4m + 3 sphere.
Contact topology and holomorphic invariants via elementary combinatorics
TL;DR: In this paper, the authors give a brief introduction to some of the ideas of contact topology and holomorphic curves, discuss some of these elementary results, and indicate how they arise from holomorphic invariants.
Contact Structures and Geometric Topology
TL;DR: A contact structure on a manifold M of dimension 2n+1 is a tangent hyperplane field, i.e., a 2n-dimensional sub-bundle of the tangent bundle as discussed by the authors.