Contact and Symplectic Topology

Front Cover
Frédéric Bourgeois, Vincent Colin, András Stipsicz
Springer Science & Business Media, Mar 10, 2014 - Science - 530 pages

Symplectic and contact geometry naturally emerged from the
mathematical description of classical physics. The discovery of new
rigidity phenomena and properties satisfied by these geometric
structures launched a new research field worldwide. The intense
activity of many European research groups in this field is reflected
by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.

 

Selected pages

Contents

Vladimir Igorevich Arnold and the Invention of Symplectic Topology
1
Topological Methods in 3Dimensional Contact Geometry
26
A Beginners Introduction to Fukaya Categories
85
Geometric Decompositions of Almost Contact Manifolds
137
Higher Dimensional Contact Topology via Holomorphic Disks
173
Contact Invariants in Floer Homology
245
Notes on Bordered Floer Homology
274
Existence and Flexibility
357
Lecture Notes on Embedded Contact Homology
389
A Topological Introduction to Knot Contact Homology
485
Copyright

Other editions - View all

Contact and Symplectic Topology
Frédéric Bourgeois,Vincent Colin,András Stipsicz
No preview available - 2016
Contact and Symplectic Topology
Frédéric Bourgeois,Vincent Colin,András Stipsicz
No preview available - 2014
Contact and Symplectic Topology
Frédéric Bourgeois,Vincent Colin,András Stipsicz
No preview available - 2014

Common terms and phrases

3-manifold boundary bundle chain complex characteristic foliation closed cobordism cohomology combinatorial compact complex structure component compute connected contact form contact manifold contact structure convex coordinates corresponding critical points define definition denote diffeomorphism differential dimension discs dividing set Eliashberg embedded equation example Exercise Figure finite foliation follows Fukaya category Geom geometry given Gromov Hamiltonian Heegaard diagram Heegaard Floer homology holomorphic currents holomorphic curves holomorphic disks homology class homotopy intersection invariant isomorphism isotopy J-holomorphic knot contact homology knot DGA Lagrangian submanifolds Legendrian foliation Lemma Math moduli space neighborhood obtain open book decomposition oriented overtwisted Ozsváth pair perturbation pointed matched circle proof Proposition quasi-contact Reeb orbits Section Seiberg-Witten sequence singular smooth sphere Stein structures surface symplectic filling symplectic manifold Symplectic Topology Theorem theory Topol torus transverse trivial vector field zero

Bibliographic information

TitleContact and Symplectic Topology
Volume 26 of Bolyai Society Mathematical Studies
EditorsFrédéric Bourgeois, Vincent Colin, András Stipsicz
Editionillustrated
PublisherSpringer Science & Business Media, 2014
ISBN3319020366, 9783319020365
Length530 pages
Subjects ›  › 

Mathematics / Applied
Mathematics / Geometry / General
Science / Physics / General
Science / Physics / Mathematical & Computational
  
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