Relative Gromov-Witten invariants

Annals of Mathematics

Volumn 157, Issue 1, 2003, Pages 45-96

  Ionel, Eleny Nicoleta ^a   Parker, Thomas H ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037224797     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2003.157.45     Document Type: Article

References (30)

1. [A] N. ARONSZAJN, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math Pures Appl. 36 (1957), 235-249.
2. [CH] L. CAPORASO and J. HARRIS, Counting plane curves of any genus, Invent. Math. 131 (1998), 345-392.
3. [E] Y. ELIASHBERG, Invariants in contact topology, Proc. Internat. Congress of Math. II (Berlin, 1998), Doc. Math. (1998) Extra Vol. II (1998), 327-338.
4. [FO] K. FUKAYA and K. ONO, Arnold conjecture and Gromov-Witten invariant, Topology 38 (1999), 933-1048.
5. [G] M. GROMOV, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347.
6. [GH] P. GRIFFITH and J. HARRIS, Principles of Algebraic Geometry, J. Wiley & Sons Inc., New York, 1978.
7. [H] C. HUMMEL, Gromov's Compactness Theorem for Pseudo-Holomorphic Curves, Progr. in Math. 151, Birkhäuer Verlag, Basel, 1997.
8. [Hu] A. HURWITZ, Uber die Anzahl der Riemann'sehen Fläechen mit gegeben Verzweigungs-plunkten, Math. Ann. 55 (1902), 53-66.
9. [IP1] E. IONEL and T. PARKER, The Gromov invariants of Ruan-Tian and Taubes, Math. Res. Lett. 4 (1997). 521-532.
10. [IP2] _, Gromov invariants and symplectic maps, Math. Ann. 314 (1999), 127-158.
11. [IP3] _, Gromov-Witten invariants of symplectic sums, Math. Res. Lett. 5 (1998), 563i-576.
12. [IP4] _, The symplectic sum formula for Gromov-Witten invariants, Ann. of Math., to appear; preprint, math.SG/0010217.
13. [IP5] _, The virtual fundamental class of the moduli space of pseudo-holomorphic maps, in preparation.
14. [IS] S. IVASHKOVICH and V. SHEVCHISHIN, Complex curves in almost-complex manifolds and meromorphic hulls, preprint, CV/9912046.
15. [K] U. KOSCHORKE, Infinite Dimensional K-Theory and Characteristic Classes of Fredholm Bundle Maps, in Global Analysis, Proc. Symposia Pure Math. XV, A. M. S., Providence, R.I., 1970, 95-133.
16. [KM] P. KRONHEIMER and T. MROWKA, Embedded surfaces and the structure of Donaldson's polynomial invariants, J. Differential Geom. 41 (1995), 573-734.
17. [LR] A.-M. Li and Y. RUAN, Symplectic surgery and Gromov-Witten invariants of Calabi-Yau 3-folds I, Invent. Math. 145 (2001), 151-218; alg-geom/9803036.
18. [LT] J. Li and G. TIAN, Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds, in Topics in Symplectic 4-Manifolds (Irvine, CA, 1996), 47-83, First Internat. Press Lect. Ser. I, International Press, Cambridge. MA, 1998.
19. [L] R. LOCKHART, Fredholm, Hodge and Liouville theorems on noncompact manifolds, Trans. A. M. S. 301 (1987). 1-35.
20. [Lo] E. LOOIJENGA, Smooth Deligne-Mumford compactifications by means of Prym level structures, J. Algebraic Geom. 3 (1994), 283-293.
21. [M] D. McDUFF, The local behaviour of holomorphic curves in almost complex 4-manifolds, J. Differential Geom. 34 (1991), 143-164.
22. [MS] D. McDUFF and D. SALAMON, J-holomorphic Curves and Quantum Cohomology, A.M.S., Providence, RI, University Lecture Series 6, 1994.
23. [P] T. PARKER, Compactified moduli spaces of pseudo-holomorphic curves, in Mirror Symmetry, III (Montreal, PQ, 1995), 77-113, AMS/IP Stud. Adv. Math. 10, A. M. S., Providence, RI, 1999.
24. [PW] T. PARKER and J. WOLFSON, Pseudo-holomorphic maps and bubble trees, J. Geom. Anal. 3 (1993) 63-98.
25. [R] Y. RUAN, Virtual neighborhoods and pseudo-holomorphic curves, Proc. of 6th Gokova Geometry-Topology Conference, Turkish J. Math. 23 (1999), 161-231.
26. [RT1] Y. RUAN and G. TIAN, A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995), 259-367.
27. [RT2] _, Higher genus symplectic invariants and sigma models coupled with gravity, Invent. Math. 130 (1997), 455-516.
28. [S] B. SIEBERT, Symplectic Gromov-Witten invariants, in New Trends in Algebraic Geometry (Warwick, 1996), 375-424, London Math. Soc. Lecture Note Ser. 264, Cambridge Univ. Press, Cambridge, 1999.
29. [SY] Y.-T. SIU and S.-T. YAU, Compact Kähler manifolds of positive bisectional curvature, Invent. Math. 59 (1980), 189-204.
30. [T] C. H. TAUBES, Counting pseudo-holomorphic curves in dimension 4, J. Differential Geom. 44 (1996), 818-893.