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Lagrangian topology and enumerative geometry

Paul Biran and Octav Cornea

Geometry & Topology 16 (2012) 963–1052
1 L Abrams, Frobenius algebra structures in topological quantum field theory and quantum cohomology, PhD thesis, The Johns Hopkins University (1997)
2 L Abrams, The quantum Euler class and the quantum cohomology of the Grassmannians, Israel J. Math. 117 (2000) 335 MR1760598
3 M Audin, Torus actions on symplectic manifolds, Progress in Math. 93, Birkhäuser (2004) MR2091310
4 M Audin, M Damian, Théorie de Morse et homologie de Floer, Savoirs Actuels (Les Ulis), EDP Sciences (2010) MR2839638
5 M Audin, F Lalonde, L Polterovich, Symplectic rigidity: Lagrangian submanifolds, from: "Holomorphic curves in symplectic geometry" (editors M Audin, J Lafontaine), Progr. Math. 117, Birkhäuser (1994) 271 MR1274934
6 D Auroux, Mirror symmetry and $T$–duality in the complement of an anticanonical divisor, J. Gökova Geom. Topol. 1 (2007) 51 MR2386535
7 D Auroux, Special Lagrangian fibrations, mirror symmetry and Calabi–Yau double covers, from: "Géométrie différentielle, physique mathématique, mathématiques et société, I", Astérisque 321, Soc. Math. France (2008) 99 MR2521645
8 D Auroux, Special Lagrangian fibrations, wall-crossing, and mirror symmetry, from: "Surveys in differential geometry. Vol. XIII. Geometry, analysis, and algebraic geometry: forty years of the Journal of Differential Geometry" (editors H D Cao, S T Yau), Surv. Differ. Geom. 13, Int. Press (2009) 1 MR2537081
9 A Banyaga, D Hurtubise, Lectures on Morse homology, Kluwer Texts in the Math. Sciences 29, Kluwer (2004) MR2145196
10 V V Batyrev, Quantum cohomology rings of toric manifolds, from: "Journées de Géométrie Algébrique d'Orsay (Orsay, 1992)", Astérisque 218, Soc. Math. France (1993) 9 MR1265307
11 P Biran, O Cornea, Lagrangian topology and enumerative geometry arXiv:1011.2271
12 P Biran, O Cornea, Quantum structures for Lagrangian submanifolds arXiv:0708.4221
13 P Biran, O Cornea, A Lagrangian quantum homology, from: "New perspectives and challenges in symplectic field theory" (editors M Abreu, F Lalonde, L Polterovich), CRM Proc. Lecture Notes 49, Amer. Math. Soc. (2009) 1 MR2555932
14 P Biran, O Cornea, Rigidity and uniruling for Lagrangian submanifolds, Geom. Topol. 13 (2009) 2881 MR2546618
15 C H Cho, Holomorphic discs, spin structures, and Floer cohomology of the Clifford torus, Int. Math. Res. Not. 2004 (2004) 1803 MR2057871
16 C H Cho, Products of Floer cohomology of torus fibers in toric Fano manifolds, Comm. Math. Phys. 260 (2005) 613 MR2183959
17 C H Cho, Non-displaceable Lagrangian submanifolds and Floer cohomology with non-unitary line bundle, J. Geom. Phys. 58 (2008) 1465 MR2463805
18 C H Cho, Y G Oh, Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds, Asian J. Math. 10 (2006) 773 MR2282365
19 R L Cohen, J D S Jones, A homotopy theoretic realization of string topology, Math. Ann. 324 (2002) 773 MR1942249
20 B Crauder, R Miranda, Quantum cohomology of rational surfaces, from: "The moduli space of curves (Texel Island, 1994)" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 33 MR1363053
21 A Dold, Lectures on algebraic topology, Grundl. Math. Wissen. 200, Springer (1980) MR606196
22 Y Felix, J C Thomas, M Vigué-Poirrier, The Hochschild cohomology of a closed manifold, Publ. Math. Inst. Hautes Études Sci. (2004) 235 MR2075886
23 K Fukaya, Floer homology and mirror symmetry, I, from: "Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (Cambridge, MA, 1999)" (editors C Vafa, S T Yau), AMS/IP Stud. Adv. Math. 23, Amer. Math. Soc. (2001) 15 MR1876064
24 K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian Floer theory and mirror symmetry on compact toric manifolds arXiv:1009.1648v1
25 K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian Floer theory on compact toric manifolds II: Bulk deformations arXiv:0810.5654
26 K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian intersection Floer theory: anomaly and obstruction. Parts I–II, AMS/IP Studies in Advanced Math. 46, Amer. Math. Soc. (2009) MR2553465
27 K Fukaya, Y G Oh, H Ohta, K Ono, Lagrangian Floer theory on compact toric manifolds, I, Duke Math. J. 151 (2010) 23 MR2573826
28 W Fulton, Introduction to toric varieties, Annals of Math. Studies 131, Princeton Univ. Press (1993) MR1234037
29 M Gerstenhaber, On the deformation of rings and algebras, Ann. of Math. 79 (1964) 59 MR0171807
30 A B Givental, Homological geometry and mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994)" (editor S D Chatterji), Birkhäuser (1995) 472 MR1403947
31 A Givental, Elliptic Gromov–Witten invariants and the generalized mirror conjecture, from: "Integrable systems and algebraic geometry (Kobe/Kyoto, 1997)", World Sci. Publ. (1998) 107 MR1672116
32 A B Givental, Private communication (March 2010)
33 A Granville, Private communication (October 2010)
34 D Hilbert, Theory of algebraic invariants, Cambridge Univ. Press (1993) MR1266168
35 K Hori, Linear models of supersymmetric D–branes, from: "Symplectic geometry and mirror symmetry (Seoul, 2000)", World Sci. Publ. (2001) 111 MR1882329
36 M Kontsevich, Homological algebra of mirror symmetry, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994)" (editor S D Chatterji), Birkhäuser (1995) 120 MR1403918
37 A Makhlouf, A comparison of deformations and geometric study of varieties of associative algebras, Int. J. Math. Math. Sci. (2007) 24 MR2295742
38 D McDuff, D Salamon, Introduction to symplectic topology, Oxford Math. Monogr., The Clarendon Press, Oxford Univ. Press (1998) MR1698616
39 D McDuff, D Salamon, $J$–holomorphic curves and symplectic topology, Amer. Math. Soc. Colloquium Publ. 52, Amer. Math. Soc. (2004) MR2045629
40 Y Ostrover, I Tyomkin, On the quantum homology algebra of toric Fano manifolds, Selecta Math. 15 (2009) 121 MR2511201
41 D Salamon, Morse theory, the Conley index and Floer homology, Bull. London Math. Soc. 22 (1990) 113 MR1045282
42 G Scheja, U Storch, Über Spurfunktionen bei vollständigen Durchschnitten, J. Reine Angew. Math. 278/279 (1975) 174 MR0393056
43 M Schwarz, Morse homology, Progress in Math. 111, Birkhäuser (1993) MR1239174
44 C Vafa, K Hori, Mirror symmetry arXiv:hep-th/0002222v3