String equation and quantum cohomology for noncompact symplectic manifolds
type: Item
instance of: scholarly article
title: String equation and quantum cohomology for noncompact symplectic manifolds
zbMATH Open document ID: 1057.53066
author: Guangcun Lu
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2004-08-20T00:00:00Z
review text: In this note the author continues to investigate the properties of the Gromov-Witten invariants of noncompact, geometrically bounded symplectic varieties, which he had defined in [\textit{G.~Lu}, C. R. Math. Acad. Sci. Paris 338, No. 11, 885--888 (2004; Zbl 1057.53054)]. He defines gravitational correlators with coefficients in the Novikov ring, and proves that their generating function fulfills the generalized string and dilaton equations. In the case of compact symplectic manifolds, the result is due to [\textit{Y.~Ruan} and \textit{G.~Tian}, Invent. Math. 130, No. 3, 455--516 (1997; Zbl 0904.58066)]. Under the further assumption that the cohomology of the manifold is finite dimensional, the author proves that the Gromov-Witten potential obeys the WDVV equation, so that is possible to define a quantum ring structure on the cohomology.
reviewed by: Mihai Halic
Mathematics Subject Classification ID: 53D45
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 81T30
zbMATH DE Number: 2094001
zbMATH Keywords: Gromov-Witten invariants
zbMATH Keywords: string equation
zbMATH Keywords: dilaton equation
zbMATH Keywords: WDVV equation
zbMATH Keywords: quantum cohomology
MaRDI profile type: Publication
full work available at URL: j.crma.2004.03.033
OpenAlex ID: W2068586649
cites work: Gromov-Witten invariants of noncompact symplectic manifolds
cites work: Higher genus symplectic invariants and sigma models coupled with gravity
cites work: Q4012873
DOI: 10.1016/J.CRMA.2004.03.033
description: scientific article; zbMATH DE number 2094001