Cobordisms of symplectic and contact manifolds
type: Item
instance of: scholarly article
title: Cobordisms of symplectic and contact manifolds
zbMATH Open document ID: 0708.57014
DOI: 10.1007/BF01078778
publication date: 1989-01-01T00:00:00Z
review text: The author introduces quasisymplectic \((2n+1)\)-dimensional manifolds, and using them he defines the group \({\mathcal B}_{2n}\) of 2n-dimensional symplectic cobordisms and the group \({\mathcal B}^{{\mathbb{Z}}}_{2n}\) of 2n- dimensional integral symplectic cobordisms. (The integral symplectic manifold (B,\(\Omega\)) is such that \(\Omega\) defines an element from \(H^ 2(B,{\mathbb{Z}}).)\) He proves that \({\mathcal B}_ 2={\mathbb{Z}}\oplus {\mathbb{R}}\), and \({\mathcal B}_ 2^{{\mathbb{Z}}}={\mathbb{Z}}\oplus {\mathbb{Z}}\). Further he introduces quasicontact 2n-dimensional manifolds and defines the group \({\mathcal C}_{2n+1}\) of contact cobordisms. The construction, called compact contactization of an integral symplectic structure, enables him to define a homomorphism \(\kappa\) : \({\mathcal B}^{{\mathbb{Z}}}_{2n}\to {\mathcal C}_{2n+1}\). He shows that \(\kappa =0\). In the end the author presents some more special results concerning the standard contact structure on the sphere bundle of the cotangent bundle over a manifold.
reviewed by: Jiří Vanžura
Mathematics Subject Classification ID: 57R90
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 57R15
zbMATH DE Number: 4163754
zbMATH Keywords: quasisymplectic manifolds
zbMATH Keywords: quasicontact manifolds
zbMATH Keywords: symplectic cobordisms
zbMATH Keywords: integral symplectic cobordisms
zbMATH Keywords: contact cobordisms
zbMATH Keywords: standard contact structure on the sphere bundle of the cotangent bundle over a manifold
author: Viktor L. Ginzburg
MaRDI profile type: Publication
cites work: Some global properties of contact structures
cites work: Cobordism and the Euler number
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4163754