Contact surgery and symplectic handlebodies
type: Item
instance of: scholarly article
title: Contact surgery and symplectic handlebodies
zbMATH Open document ID: 0737.57012
author: Alan Weinstein
published in: Hokkaido Mathematical Journal
publication date: 1992-06-25T00:00:00Z
review text: \textit{C. Meckert} [Ann. Inst. Fourier 32, No. 3, 251-260 (1982; Zbl 0471.58001)] has shown that the connected sum of two contact manifolds has a contact structure. The author of the paper extends Meckert's result as follows. Let \(Y\) be any isotropic sphere in a contact manifold \(X\), with a trivialization of the conformal symplectic normal bundle of \(Y\) (the conformal symplectic normal bundle is a direct summand of the ordinary normal bundle of \(Y\) in \(X\)). Then the manifold \(X'\) obtained from \(X\) by elementary surgery along \(Y\) (using the framing induced by the trivialization) has a contact structure. Moreover, \(X\) and \(X'\) both form the boundary of an elementary cobordism \(P\) having a symplectic structure together with a conformally symplectic vector field which is transverse to the boundary and which actually produces the original contact structure on \(X\) and the contact structure on \(X'\).
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 57R25
Mathematics Subject Classification ID: 57R65
zbMATH DE Number: 11093
zbMATH Keywords: isotropic sphere in a contact manifold
zbMATH Keywords: conformal symplectic normal bundle
zbMATH Keywords: manifold obtained by elementary surgery
zbMATH Keywords: elementary cobordism having a symplectic structure
zbMATH Keywords: conformally symplectic vector field
reviewed by: Krzysztof Pawałowski
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1381413841
OpenAlex ID: W2036331318
DOI: 10.14492/HOKMJ/1381413841
description: scientific article; zbMATH DE number 11093