Cohomologie quantique

Audin, Michèle

Séminaire Bourbaki : volume 1995/96, exposés 805-819, Astérisque, no. 241 (1997), Exposé no. 806, 30 p.

[1] P. Aspinwall, D. Morrison, Topological field theory and rational curves, Commun. Math. Phys. 151 (1993), 245-262. | DOI | MR | Zbl

[2] A. Astachkevich, V. Sadov, Quantum cohomology of partial flag manifolds, Commun. Math. Phys. 170 (1995), 503-528. | DOI | MR | Zbl

[3] M. Audin, Symplectic and almost complex manifolds, in [4].

[4] M. Audin, J. Lafontaine, EDS, Holomorphic curves in symplectic geometry, Progress in Math. 117, Birkhäuser, 1994. | MR | Zbl

[5] M. Audin, F. Lalonde, L. Polterovich, Symplectic rigidity: Lagrangian submanifolds, in [4].

[6] V. Batyrev, Quantum cohomology ring of toric manifolds, Astérisque 218 (1993), 9-34. | MR | Zbl

[7] A. Beauville, Conformal blocks, fusion rules and the Verlinde formula, Israel Math. Conferences Proc. 9 (1996), 75-96. | MR | Zbl

[8] A. Beauville, Quantum cohomology of complete intersections, Математическая физика, анализ, геометрия 2 (1995), 384-398. | Zbl

[9] K. Behrend, GW-invariants in algebraic geometry, preprint (1996).

[10] K. Behrend, B. Fantechi, The intrinsic normal cone, preprint (1996). | MR | Zbl

[11] A. Bertram, Modular Schubert calculus, Advances in Math. (à paraître).

[12] A. Bertram, G. Daskalopoulos, R. Wentworth, Gromov invariants for holomorphic maps from Riemann surfaces to Grassmannians, Journ. Amer. Math. Soc. 9 (1996), 529-571. | DOI | MR | Zbl

[13] P. Candelas, X. De La Ossa, P. Green, L. Parkes, A pair of Calabi- Yau manifolds as an exactly soluble superconformal field theory, Nucl. Phys. B359 (1991), 21-74. | DOI | Zbl

[14] I. Ciocan-Fontanine, Quantum cohomology of flag varieties, IMRN 6 (1995), 263-277. | DOI | MR | Zbl

[15] B. Crauder, R. Miranda, Quantum cohomology of rational surfaces, in [17]. | DOI | Zbl

[16] P. Di Francesco, C. Itzykson, Quantum intersection rings, in [17]. | DOI | Zbl

[17] R. Dijkgraaf, C. Faber, G. Van Der Geer, EDS, The moduli space of curves, Progress in Math. 129, Birkhäuser, 1995. | MR | Zbl

[18] S. Donaldson, The orientation of Yang-Mills moduli spaces and 4-manifold topology, J. Diff. Geom. 26 (1987), 397-428. | DOI | MR | Zbl

[19] S. Donaldson, P. Kronheimer, The geometry of four-manifolds, Oxford University Press, 1990. | MR | Zbl

[20] B. Dubrovin, Integrable systems and classification of 2-dimensional topological field theories in Integrable systems, the Verdier memorial conference, edited by O. BABELON, P. CARTIER, Y. KOSMANN-SCHWARZBACH, Progress in Math. 115, Birkhäuser, 1994, et Geometry of 2D topological field theories, Lecture Notes in Math. 1620, Springer, 1995. | MR | Zbl

[21] A. Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), 575-611. | DOI | MR | Zbl

[22] K. Fukaya, K. Ono, Arnold conjecture and Gromov-Witten invarient (sic), preprint (1996). | MR | Zbl

[23] W. Fulton, R. Pandharipande, Notes on stable maps and quantum cohomology, preprint (1996). | MR | Zbl

[24] P. Gauduchon, Connexions linéaires, classes de Chern, théorème de Riemann-Roch, in [4]. | DOI

[25] A. Givental, Homological geometry and mirror symmetry, in I.C.M. Zürich (1994), Birkhäuser, 1995, 473-480. | MR | Zbl

[26] A. Givental, Equivariant Gromov-Witten invariants, IMRN (1996, à paraître). | MR | Zbl

[27] A. Givental, B. Kim, Quantum cohomolgy of flag manifolds and Toda lattices, Commun. Math. Phys. 168 (1995), 609-641. | DOI | MR | Zbl

[28] M. Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. | DOI | EuDML | MR | Zbl

[29] N. Hitchin, Frobenius manifolds, in Gauge Theory and Symplectic Geometry, Séminaire de Mathématiques Supérieures, Montréal, 1995, Kluwer, à paraître. | MR | Zbl

[30] H. Hofer, V. Lizan, J.-C. Sikorav, On genericity for holomorphic curves in 4-dimensional almost-complex manifolds, The Journ. of Geom. Anal. (à paraître). | MR | Zbl

[31] H. Hofer, D. Salamon, Floer homology and Novikov rings, in the Floer memorial volume, Progress in Math. 133, Birkhäuser, 1995. | MR | Zbl

[32] C. Itzykson, Counting rational curves on rational surfaces, preprint (1994). | DOI | MR | Zbl

[33] M. Kontsevich, Enumeration of rational curves via torus actions, in [17]. | DOI | Zbl

[34] M. Kontsevich, Mirror symmetry in dimension 3, in Séminaire Bourbaki 1994- 95, Astérisque 237 (1996). | EuDML | Numdam | MR | Zbl

[35] M. Kontsevich, Yu. Manin, Gromov-Witten classes, quantum cohomology and enumerative geometry, Commun. Math. Phys. 164 (1994), 525-562. | DOI | MR | Zbl

[36] D. Kotschick, The Seiberg-Witten invariants of symplectic four-manifolds [after C. H. Taubes], in Séminaire Bourbaki 1995-96, Astérisque, ce volume. | EuDML | Numdam | MR | Zbl

[37] F. Lalonde, D. Mcduff, The classification of ruled symplectic 4-manifolds, Math. Res. Letters (1996), à paraître. | MR | Zbl

[38] J. Li, G. Tian, The quantum cohomology of homogeneous varieties, preprint (1995). | MR | Zbl

[39] J. Li, G. Tian, Virtual moduli cycles and $GW$-invariants, preprint (1996).

[40] G. Liu, Associativity of quantum multiplication, preprint (1995). | MR | Zbl

[41] Yu. Manin, Generating functions in algebraic geomerty and sums over trees, in [17]. | Zbl

[42] D. Mcduff, Examples of symplectic structures, Invent. Math. 89 (1987), 13-36. | DOI | EuDML | MR | Zbl

[43] D. Mcduff, The structure of rational and ruled symplectic $4$-manifolds, Journ. Amer. Math. Soc. 3 (1990), 679-712. | MR | Zbl

[44] D. Mcduff, Singularities and positivity of intersections of $J$-holomorphic curves, in [4]. | DOI | MR

[45] D. Mcduff, D. Salamon, $J$-holomorphic curves and quantum cohomology, Amer. Math. Soc., 1994, retirage corrigé, 1995. | MR | Zbl

[46] D. Morrison, Mirror symmetry and rational curves on quintic threefolds: a guide for mathematicians, Journ. Amer. Math. Soc. 6 (1993), 223-247. | DOI | MR | Zbl

[47] S. Novikov, Multivalued functions and functionals - an analogue of the Morse theory, Soviet Math. Dokl. 24 (1981), 222-225. | MR | Zbl

[48] P. Pansu, Compactness, in [4]. | DOI

[49] S. Piunikhin, D. Salamon, M. Schwarz, Symplectic Floer-Donaldson theory and quantum cohomology, preprint (1995). | MR | Zbl

[50] Y. Ruan, Symplectic topology on algebraic 3-folds, Journal of Diff. Geometry 39 (1994), 215-227. | DOI | MR | Zbl

[51] Y. Ruan, G. Tian, A mathematical theory of quantum cohomology (annonce), Math. Res. Letters 1 (1994), 269-278, et A mathematical theory of quantum cohomology, Journal of Diff. Geometry 42 (1995), 259-367. | DOI | MR | Zbl

[52] B. Siebert, Gromov-Witten invariants for general symplectic manifolds, preprint (1996). | MR

[53] B. Siebert, G. Tian, On quantum cohomology rings of Fano manifolds and a formula of Vafa and Intriligator, preprint (1994). | MR | Zbl

[54] C. H. Taubes, The Seiberg-Witten and the Gromov Invariants, Math. Res. Letters 2 (1995), 221-238. | DOI | MR | Zbl

[55] G. Tian, Quantum cohomology and its associativity, preprint (1995). | MR | Zbl

[56] C. Vafa, Topological mirrors and quantum rings, in Essays on Mirror manifolds, S. T. Yau Ed., International Press, Hong-Kong, 1992. | MR | Zbl

[57] C. Voisin, Symétrie miroir, Panoramas et Synthèses, volume 2, Société Mathématique de France, 1996. | MR | Zbl

[58] C. Voisin, A mathematical proof of Aspinwall-Morrison formula, Compositio Math. (à paraître). | Numdam | Zbl

[59] E. Witten, Two dimensional gravity and intersection theory on moduli space, Surveys in Diff. Geometry 1 (1991), 243-310. | DOI | MR | Zbl

[60] E. Witten, The Verlinde algebra and the cohomology of the Grassmannian, preprint (1993). | MR | Zbl