Topology/Mathematical Physics
String equation and quantum cohomology for noncompact symplectic manifolds
Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 941-944.

We use our Gromov–Witten invariant theory in a previous Note for noncompact geometrically bounded symplectic manifolds to get solutions of the generalized string equation and dilation equation and their variants. More solutions of the WDVV equation and quantum products on cohomology groups are also obtained for the symplectic manifolds with finitely dimensional cohomology groups.

En utilisant la théorie des invariants de Gromov–Witten dans une Note précédente pour variétés symplectiques non compactes, géométriquement bornées, on obtient des solutions de l'équation généralisée des cordes, de l'équation de dilatation et de leurs variantes. On obtient également davantage de solutions de l'équation WDVV et des produits de quantum sur les groupes de cohomologie, pour les variétés symplectiques dont les groupes de cohomologie sont de dimension finie.

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Published online:
DOI: 10.1016/j.crma.2004.03.033
Lu, Guangcun 1

1 Department of Mathematics, Beijing Normal University, Beijing 100875, PR China
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Lu, Guangcun. String equation and quantum cohomology for noncompact symplectic manifolds. Comptes Rendus. Mathématique, Volume 338 (2004) no. 12, pp. 941-944. doi : 10.1016/j.crma.2004.03.033. http://www.numdam.org/articles/10.1016/j.crma.2004.03.033/

[1] Lu, G. Gromov–Witten invariants of noncompact symplectic manifolds, C. R. Acad. Sci. Paris, Ser. I, Volume 338 (2004)

[2] Lu, G. Virtual moduli cycles and Gromov–Witten invariants of noncompact symplectic manifolds (17 June, revised V2, 1 August 2003) | arXiv

[3] Ruan, Y.; Tian, G. A mathematical theory of quantum cohomology, J. Differential Geom., Volume 43 (1995) no. 2

[4] Ruan, Y.; Tian, G. Higher genus symplectic invariants and sigma model coupled with gravity, Invent. Math., Volume 130 (1997), pp. 455-516

[5] Witten, E. Two dimensional gravity and intersection theory on moduli space, Surveys Differential Geom., Volume 1 (1991), pp. 243-310

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