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Virtual Manifolds and Localization

Virtual Manifolds and Localization
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摘要 In this paper, we explore the virtual technique that is very useful in studying the moduli problem from a differential geometric point of view. We introduce a class of new objects ＂virtual manifolds/orbifolds＇, on which we develop the integration theory. In particular, the virtual localization formula is obtained. In this paper, we explore the virtual technique that is very useful in studying the moduli problem from a differential geometric point of view. We introduce a class of new objects ＂virtual manifolds/orbifolds＇, on which we develop the integration theory. In particular, the virtual localization formula is obtained.
作者 Bohui CHEN Gang TIAN
机构地区 Department of Mathematics and Yangtze Mathematical Center Department of Mathematics Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第1期1-24,共24页 数学学报（英文版）
基金 supported by an NSF key project a 973 project 2006CB805900
关键词 virtual manifolds LOCALIZATION Fredholm system moduli space virtual manifolds, localization, Fredholm system, moduli space
分类号 TP391.9 [自动化与计算机技术—计算机应用技术] O189.31 [理学—基础数学]
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参考文献13

  • 1Atiyah, M. F., Bott, R.: The moment map and equivariant cohomology. Topology, 23(1), 1-28 (1984).
  • 2Ruan, Y.: Topological sigma model and Donaldson-type invariants in Gromov theory. Duke Math. J., 83(2), 461-500 (1996).
  • 3Ruan, Y., Tian, G.: A mathematical theory of quantum cohomology. J. Differential Geom., 42(2), 259-367 (1995).
  • 4Ruan, Y., Tian, G.: Higher genus symplectic invariants and sigma models coupled with gravity. Invent. Math., 130(3), 455-516 (1997).
  • 5Fukaya, K., Ono, K.: Arnold conjecture and Gromov-Witten invariant. Topology, 38(5), 933-1048 (1999).
  • 6Li, J., Tian, G.: Virtual moduli cycles and Gromov-Witten invariants of algebraic varieties. J. Amer. Math. Soc., 11(1), 119 174 (1998).
  • 7Li, J., Tian, G.: Virtual moduli cycles and Gromov Witten invariants of general symplectic manifolds. Topics in symplectic 4-manifolds (Irvine, CA, 1996), 47-83, First Int. Press Lect. Ser., I, Internat. Press, Cambridge, MA, 1998.
  • 8Liu, G., Tian, G.: Floer homology and Arnold conjecture. J. Differential Geom., 49(1), 1-74 (1998).
  • 9Ruan, Y.: Virtual neighborhoods and pseudo-holomorphic curves. In: Proceedings of 6th G kova Geometry- Topology Conference. Turkish J. Math., 23(1), 161-231 (1999).
  • 10Chen, B., Li, A.: Symplectic virtual localization of Gromov-Witten invariants, preprint.
Acta Mathematica Sinica,English Series
2010年 第1期

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