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Mathematics > Symplectic Geometry

arXiv:math/0609483 (math)
[Submitted on 18 Sep 2006]

Title:Degeneration and gluing of Kuranishi structures in Gromov-Witten theory and the degeneration/gluing axioms for open Gromov-Witten invariants under a symplectic cut

Authors:Chien-Hao Liu, Shing-Tung Yau
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Abstract: We study the degeneration and the gluing of Kuranishi structures in Gromov-Witten theory under a symplectic cut. This leads us to a degeneration axiom and a gluing axiom for open Gromov-Witten invariants. They provide then a route to the construction of virtual fundamental chains via specialization. Comments on the equivalence of the degeneration formula of closed Gromov-Witten invariants by Li-Ruan/Li versus Ionel-Parker are given in the Appendix.
Comments: 102+2 pages
Subjects: Symplectic Geometry (math.SG); High Energy Physics - Theory (hep-th); Algebraic Geometry (math.AG)
MSC classes: 53D45; 14N35, 81T30
Cite as: arXiv:math/0609483 [math.SG]
  (or arXiv:math/0609483v1 [math.SG] for this version)
  https://doi.org/10.48550/arXiv.math/0609483

Submission history

From: Chien-Hao Liu [view email]
[v1] Mon, 18 Sep 2006 03:00:03 UTC (159 KB)
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