Invariants in contact topology
type: Item
instance of: scholarly article
title: Invariants in contact topology
zbMATH Open document ID: 0913.53010
author: Yakov Eliashberg
published in: Documenta Mathematica
publication date: 1998-08-06T00:00:00Z
full work available at URL: https://eudml.org/doc/231306
full work available at URL: Eliashberg.MAN.html
review text: It is known that all 3-dimensional contact manifolds are divided into two complementary classes: tight and overtwisted. The overtwisted contact structures on 3-manifolds are classified up to isotopy by their formal homotopy classes. Until very recently, there was known only one result allowing to distinguish contact structures on manifolds of dimension \(> 3\) within a given formal homotopy class: for any \(n > 2\), the sphere \(S^{2n-1}\) has a contact structure \(\xi_1\) in the standard formal homotopy class, which is not isomorphic to the standard structure \(\xi_0\). The main goal of this paper is the construction of new algebraic invariants, related to Gromov-Witten invariants of symplectic manifolds, which would allow to distinguish contact manifolds in the same formal homotopy class. For this purpose, the graded contact homology algebra of a contact manifold \((V,\xi)\) is constructed and investigated.
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 55N35
zbMATH DE Number: 1184332
zbMATH Keywords: contact manifolds
zbMATH Keywords: symplectization
zbMATH Keywords: holomorphic curves
zbMATH Keywords: set of all periodic trajectories
zbMATH Keywords: contact homology algebra
zbMATH Keywords: Legendrian submanifolds
reviewed by: Nicolai K. Smolentsev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184332