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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Guangcun Lu 1
@article{CRMATH_2004__338_12_941_0, author = {Guangcun Lu}, title = {String equation and quantum cohomology for noncompact symplectic manifolds}, journal = {Comptes Rendus. Math\'ematique}, pages = {941--944}, publisher = {Elsevier}, volume = {338}, number = {12}, year = {2004}, doi = {10.1016/j.crma.2004.03.033}, language = {en}, }
Guangcun Lu. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.033/
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