Virtual Neighborhood Technique for Holomorphic Curve Moduli Spaces

2017/10/29 by Li, An-Min, Sheng, Li
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1710.10581

Abstract

In this paper we use the approach of Ruan and Li-Ruan to construct virtual neighborhoods and show that the Gromov-Witten invariants can be defined as an integral over top strata of virtual neighborhood. We prove that the invariants defined in this way satisfy all the Gromov-Witten axioms of Kontsevich and Manin.

Related

• Virtual neighborhood technique for pseudo-holomorphic spheres
• Smoothness of Kuranishi atlases on Gromov-Witten moduli spaces
• Gromov-Witten theory via Kuranishi structures
• Algebraic structures on the topology of moduli spaces of curves and maps
• Gromov-Witten invariants in family and quantum cohomology