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Contact and Symplectic Topology

Part of the Bolyai Society Mathematical Studies Book Series (volume 26)

Editors: Bourgeois, Frédéric; Colin, Vincent; Stipsicz, András

DOI: 10.1007/978-3-319-02036-5

ISBN: 978-3-319-02035-8

Publisher: Springer International Publishing - Springer Journals

Nov 19, 2013

1 - 10 of 10 Chapters

LitStream

Chapter 1Vladimir Igorevich Arnold and the Invention of Symplectic Topology

Audin, Michèle

Pages: 1 –25

[In 1965, with a Comptes rendus note of Vladimir Arnold, a new discipline, symplectic topology, was born. In 1986, its (remarkable) first steps were reported by Vladimir Arnold himself. In the meantime…]
LitStream

Chapter 2Topological Methods in 3-Dimensional Contact Geometry

Massot, Patrick

Pages: 27 –83

[These notes provide an introduction to Giroux’s theory of convex surfaces in contact 3-manifolds and its simplest applications. The first goal is to explain why all the information about a contact structure in a neighborhood of a generic surface is encoded by finitely many curves on the surface....
LitStream

Chapter 3A Beginner’s Introduction to Fukaya Categories

Auroux, Denis

Pages: 85 –136

[The goal of these notes is to give a short introduction to Fukaya categories and some of their applications. The first half of the text is devoted to a brief review of Lagrangian Floer (co)homology and product structures. Then we introduce the Fukaya category (informally and without a lot of the...
LitStream

Chapter 4Geometric Decompositions of Almost Contact Manifolds

Presas, Francisco

Pages: 137 –172

[These notes are intended to be an introduction to the use of approximately holomorphic techniques in almost contact and contact geometry. We develop the setup of the approximately holomorphic geometry. Once done, we sketch the existence of the two main geometric decompositions available for an...
LitStream

Chapter 5Higher Dimensional Contact Topology via Holomorphic Disks

Niederkrüger, Klaus

Pages: 173 –244

[The aim of this notes is to explain some non-fillability results in higher dimensional contact topology, which are closely related to the question of how to define overtwistedness. We start with an overview of some basic examples and theorems known so far, comparing them with analogous results...
LitStream

Chapter 6Contact Invariants in Floer Homology

Matić, Gordana

Pages: 245 –273

[In a pair of seminal papers Peter Ozsváth and Zoltan Szabó defined a collection of homology groups associated to a 3-manifold they named Heegaard-Floer homologies. Soon after, they associated to a contact structure ξ on a 3-manifold, an element of its Heegaard-Floer homology, the contact...
LitStream

Chapter 7Notes on Bordered Floer Homology

Lipshitz, Robert; Ozsváth, Peter; Thurston, Dylan P.

Pages: 275 –355

[Bordered Heegaard Floer homology is an extension of Ozsváth-Szabós Heegaard Floer homology to 3-manifolds with boundary, enjoying good properties with respect to gluings. In these notes we will introduce the key features of bordered Heegaard Floer homology: its formal structure, a precise...
LitStream

Chapter 8Stein Structures: Existence and Flexibility

Cieliebak, Kai; Eliashberg, Yakov

Pages: 357 –388

[This survey on the topology of Stein manifolds is an extract from the book of Cieliebak and Eliashberg (From Stein to Weinstein and Back—Symplectic Geometry of Affine Complex Manifolds, Colloquium Publications, vol. 59, 2012). It is compiled from two short lecture series given by the first...
LitStream

Chapter 9Lecture Notes on Embedded Contact Homology

Hutchings, Michael

Pages: 389 –484

[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 remarks and examples which have not been previously...
LitStream

Chapter 10A Topological Introduction to Knot Contact Homology

Ng, Lenhard

Pages: 485 –530

[Knot contact homology is a Floer-theoretic knot invariant derived from counting holomorphic curves in the cotangent bundle of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...

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