Dynamics, topology and holomorphic curves
type: Item
instance of: scholarly article
title: Dynamics, topology and holomorphic curves
zbMATH Open document ID: 0908.58020
published in: Documenta Mathematica
publication date: 1998-08-24T00:00:00Z
full work available at URL: Hofer.MAN.html
review text: The author describes the intimate interplay between certain classes of dynamical systems and a holomorphic curve theory. He emphasizes this interplay in real dimension three. The author gives a tool to construct global surfaces of section and generalizations thereof for the large class of Reeb vector fields, which includes, in particular, all geodesic flows on surfaces. (There are many aspects touching areas like Gromov-Witten invariants, quantum cohomology, symplectic homology, Seiberg-Witten invariants, Hamiltonian dynamics and more).
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 53D25
zbMATH DE Number: 1194150
zbMATH Keywords: Hamiltonian dynamics
zbMATH Keywords: contact forms
zbMATH Keywords: Reeb vector fields
zbMATH Keywords: quantum cohomology
zbMATH Keywords: Gromov-Witten invariants
zbMATH Keywords: Arnold conjecture
zbMATH Keywords: Weinstein conjecture
zbMATH Keywords: symplectic homology
zbMATH Keywords: surfaces of section
author: Helmut Hofer
reviewed by: Themistocles M. Rassias
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1194150