Topological conformal field theories and Calabi-Yau categories

Advances in Mathematics

Volumn 210, Issue 1, 2007, Pages 165-214

  Costello, Kevin ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

A infinity categories; Moduli spaces of surfaces; Topological conformal field theories

Indexed keywords

EID: 33846456192     PISSN: 00018708     EISSN: 10902082     Source Type: Journal    
DOI: 10.1016/j.aim.2006.06.004     Document Type: Article

References (38)

1. Barannikov S. Generalized periods and mirror symmetry in dimensions n > 3 (1999). math.AG/9903124
2. Barannikov S. Quantum periods I. Semi-infinite variations of Hodge structures (2000). math.AG/0006193
3. Barannikov S., and Kontsevich M. Frobenius manifolds and formality of Lie algebras of polyvector fields (1997). math.QA/9710032
4. Bershadsky M., Cecotti S., Ooguri H., and Vafa C. Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes. Comm. Math. Phys. 165 2 (1994) 311-427
5. Chas M., and Sullivan D. String topology (1999). math.GT/9911159
6. Chas M., and Sullivan D. Closed string operators in topology leading to Lie bialgebras and higher string algebra. The Legacy of Niels Henrik Abel (2004), Springer, Berlin 771-784
7. Cohen R. Morse theory, graphs and string topology (2004). math.GT/0411272
8. ∞ operad and the moduli space of curves (2004). math.AG/0402015
9. Costello K. A dual point of view on the ribbon graph decomposition of moduli space (2006). math.GT/0601130
10. K. Fukaya, Y.-G. Oh, H. Ohta, K. Ono, Lagrangian intersection Floer theory: Anomaly and obstruction, 2000
11. Getzler E. Batalin-Vilkovisky algebras and two-dimensional topological field theories. Comm. Math. Phys. 159 2 (1994) 265-285
12. Hamilton A., and Lazarev A. Homotopy algebras and noncommutative geometry (2004). math.QA/0410621
13. Kaufmann R.M. A proof of a cyclic version of Deligne's conjecture via cacti (2004). math.QA/0403340
14. Keller B. Deriving DG categories. Ann. Sci. École Norm. Sup. (4) 27 1 (1994) 63-102
15. Kontsevich M. Homological algebra of mirror symmetry. Proceedings of the International Congress of Mathematicians, vols. 1, 2. Zürich, 1994 (1995), Basel, Birkhäuser 120-139
16. Kontsevich M. Operads and motives in deformation quantization. Lett. Math. Phys. 48 1 (1999) 35-72 Moshé Flato (1937-1998)
17. M. Kontsevich, Talk at the Hodge Centennial Conference, Edinburgh, 2003
18. Kapustin A., and Rozansky L. On the relation between open and closed topological strings. Comm. Math. Phys. 252 1-3 (2004) 393-414. hep-th/0405232
19. Kontsevich M., and Soibelman Y. Deformations of algebras over operads and the Deligne conjecture. Conférence Moshé Flato 1999, vol. I. Dijon. Math. Phys. Stud. vol. 21 (2000), Kluwer Acad. Publ., Dordrecht 255-307
20. Kontsevich M., and Soibelman Y. Homological mirror symmetry and torus fibrations (2001). math.SG/0011041
21. Kimura T., Stasheff J., and Voronov A.A. On operad structures of moduli spaces and string theory. Comm. Math. Phys. 171 1 (1995) 1-25. hep-th/9307114
22. Lazaroiu C.I. On the structure of open-closed topological field theory in two dimensions. Nucl. Phys. B 603 3 (2001) 497-530. hep-th/0010269
23. 1-equivariant pair (2002). math.SG/0210257
24. ∞ (strongly associative) structures (2004). math.AT/0401007
25. Merkulov S.A. Strong homotopy algebras of a Kähler manifold. Int. Math. Res. Not. 1999 3 (1999) 153-164. math.AG/9809172
26. MacLane S. Categories for the Working Mathematician. Grad. Texts in Math. second ed. vol. 5 (1998), Springer, New York
27. Moore G. Some comments on branes, G-flux, and K-theory. Strings 2000, Proceedings of the International Superstrings Conference, vol. 16. Ann Arbor, MI (2001) 936-944
28. McClure J.E., and Smith J.H. A solution of Deligne's Hochschild cohomology conjecture. Recent Progress in Homotopy Theory. Baltimore, MD, 2000. Contemp. Math. vol. 293 (2002), Amer. Math. Soc., Providence, RI 153-193
29. Segal G. Topological field theory (1999). http://www.cgtp.duke.edu/ITP99/segal/ Notes of Lectures at Stanford University
30. Segal G. The definition of conformal field theory. Topology, Geometry and Quantum Field Theory. London Math. Soc. Lecture Note Ser. vol. 308 (2004), Cambridge Univ. Press, Cambridge 421-577 First circulated in 1988
31. Seidel P. More about vanishing cycles and mutation. Symplectic Geometry and Mirror Symmetry. Seoul, 2000 (2001), World Sci. Publishing, River Edge, NJ 429-465
32. Seidel P. Vanishing cycles and mutation. European Congress of Mathematics, vol. II. Barcelona, 2000. Progr. Math. vol. 202 (2001), Birkhäuser, Basel 65-85
33. Seidel P. Fukaya categories and deformations. Proceedings of the International Congress of Mathematicians, vol. II. Beijing, 2002 (2002), Higher Ed. Press, Beijing 351-360
34. Stasheff J.D. Homotopy associativity of H-spaces I, II. Trans. Amer. Math. Soc. 108 (1963) 275-292
35. Stasheff J.D. Homotopy associativity of H-spaces I, II. Trans. Amer. Math. Soc. 108 (1963) 293-312
36. Tamarkin D.E. Another proof of M. Kontsevich formality theorem (1998). math.QA/9803025
37. Tradler T., and Zeinalian M. On the cyclic Deligne conjecture (2004). math.QA/0404218
38. Witten E. Mirror manifolds and topological field theory (1991). hep-th/9112056