Higher genus symplectic invariants and sigma models coupled with gravity

Inventiones Mathematicae

Volumn 130, Issue 3, 1997, Pages 455-516

  Ruan, Yongbin ^a   Tian, Gang ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031508818     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002220050192     Document Type: Article

References (33)

1. g = 1, (Warwick Preprint, 1992)
2. I. Ciocan-Fontanine, Quantum cohomology of flag varieties, Preprint
3. S. Donaldson, Polynomila invariants for smooth four manifolds, Topology, 29, 257-315 (1990)
4. 1 model and the large-N matrix integral, Modern Phy Letters A. Vol. 9, No. 31, 2893-2902 (1994)
5. R. Friedman and J. Morgan, On the diffeomorphism types of certain algebraic surfaces I, II, J. Diff. Geom., 27, (1988)
6. D. Freed and K. Uhlenbeck, Instantons and four-manifolds, Springer-Verlag.
7. E. Getzler, private communications
8. M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. math., 82, 307-347 (1985)
9. H. Hori, Constraints for topological strings in D ≥ 1, preprint.
10. M. Kontsevich and Y. Manin, GW classes, Quantum cohomology and enumerative geometry, Comm.Math.Phys., 164, 525-562 (1994)
11. M. Kontsevich, Intersection theory on the moduli space of curves and the matrix airy function, Comm. Math. Phys., 147, (1992)
12. J. Li and G. Tian, Quantum cohomology of homogeneous manifolds, to appear in J. Alg. Geom.
13. C. McCory, Cone complex and PL-transversality, Trans. Amer. Math. Soc. 207, 269-291 (1975)
14. D. McDuff, Examples of symplectic structures, Invent. math., 89, 13-36 (1987)
15. D. McDuff, Notes on ruled symplectic 4-manifolds, preprint
16. D. McDuff and D. Salamon, J-holomorphic curves and quantum cohomology, University Lec. Series, vol. 6, AMS
17. J. Morgan and K O'Grady, The smooth classification of fake K3's and similar surfaces, preprint
18. J. Morgan and T. Mrowka, On the diffeomorphism classification of regular elliptic surfaces, (preprint)
19. D. Mumford, Towards an enumerative geometry of the moduli space of curves, Arithmetic and Geometry edited by M. Artin, J. Tate
20. T. Parker and J. Woflson, A compactness theorem for Gromov's moduli space, J. Geom. Analysis, 3, 63-98 (1993)
21. Y. Ruan, Topological Sigma model and Donaldson type invariants in Gromov theory, to appear in Duke Jour
22. Y. Ruan, Symplectic topology on algebraic 3-folds, Jour. Diff. Geom., 39, 215-227 (1994)
23. Y. Ruan, Symplectic topology and extremal rays, Geo. Fun, Anal. Vol 3, no 4, 395-430 (1993)
24. Y. Ruan, Symplectic topology and complex surfaces, Geometry and analysis on complex manifold edited by T. Mabuchi, J. Noguchi, T. Ochiai. World Scientific
25. Y. Ruan and G. Tian, A mathematical theory of quantum cohomology. To appear in J. Diff. Geom., 1995; announcement, Math. Res. Let., vol 1, no 1, 269-278 (1994)
26. Y. Ruan and G. Tian, A mathematical theory of quantum cohomology. To appear in J. Diff. Geom., 1995; announcement, Math. Res. Let., vol 1, no 1, 269-278 (1994)
27. Y. Ruan and G. Tian, Bott-type symplectic Floer cohomology and its multiplication structures, preprint, 1995
28. C. Taubes, The Seiberg-Witten invariants and symplectic forms, Math. Res. Letters 1, 809-822 (1995)
29. C. Taubes, The Seiberg-Witten and the Gromov invariants, preprint, 1995
30. G. Tian, The quantum cohomology and its associativity, preprint, March, 1995
31. E. Witten, Topological sigma models, Comm. Math. Phys., 118, (1988)
32. E. Witten, Two dimensional gravity and intersection theory on moduli space, Surveys in Diff. Geom., 1, 243-310 (1991)
33. R. Ye, Gromov's compactness theorem for pseudo-holomorphic curves, Trans. Amer. math. Soc., 1994, document