2003/06/30 by Guangcun Lu
Mathematics · #Bounded function #Cohomology #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Gromov–Witten invariant #Moduli #Moduli space #Quantum cohomology #Symplectic geometry #Symplectic manifold #math.DG #math.SG #msc:14Nxx #msc:53D45 #msc:57R17
paper · pdf · doi:10.1007/s00220-005-1393-7
published as Commun. Math. Phys. 261(2006), 43-131 · Final version
openalex publication_date 2005/10/06 · arxiv created 2006/05/03 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This paper constructs and studies the Gromov-Witten invariants and their properties for noncompact geometrically bounded symplectic manifolds. Two localization formulas for GW-invariants are also proposed and proved. As applications we get solutions of the generalized string equation and dilation equation and their variants. The more solutions of WDVV equation and quantum products on cohomology groups are also obtained for the symplectic manifolds with finitely dimensional cohomology groups. To realize these purposes we further develop the language introduced by Liu-Tian to describe the virtual moduli cycle (defined by Liu-Tian, Fukaya-Ono, Li-Tian, Ruan and Siebert).