Lie groupoids, deformation of unstable curves, and construction of equivariant Kuranishi charts

DOI10.4171/PRIMS/57-3-13MaRDI QIDQ824258

Kenji Fukaya

Publication date: 15 December 2021

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.02840

zbMATH Keywords

Lie groupoidGromov-Witten invariantpseudo-holomorphic curveKuranishi structureunstable curve

Mathematics Subject Classification ID

Global theory of symplectic and contact manifolds (53D35) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds (53D45) Stacks and moduli problems (14D23)

Related Items

\(T\)-equivariant disc potential and SYZ mirror construction

Cites Work

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• Shrinking good coordinate systems associated to Kuranishi structures
• Antisymplectic involution and Floer cohomology
• Quotients by groupoids
• Versal deformations and algebraic stacks
• Floer homology and Arnold conjecture
• Localization of virtual classes
• Arnold conjecture and Gromov-Witten invariant
• Gromov's compactness theorem for pseudo-holomorphic curves
• Higher genus symplectic invariants and sigma models coupled with gravity
• Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks. I
• Cyclic symmetry and adic convergence in Lagrangian Floer theory
• The irreducibility of the space of curves of a given genus
• How to conjugate C\(^1\)-close group actions
• Lagrangian Floer theory and mirror symmetry on compact toric manifolds
• Geometry of Algebraic Curves
• ON A GENERALIZATION OF THE NOTION OF MANIFOLD
• Virtual moduli cycles and Gromov-Witten invariants of general symplectic manifolds
• Virtual neighborhoods and pseudo-holomorphic curves
• Kuranishi Structures and Virtual Fundamental Chains
• Atiyah-Floer conjecture: A formulation, a strategy of proof and generalizations
• Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory
• Equivariant Gromov - Witten Invariants
• Applications of Polyfold Theory I: The Polyfolds of Gromov–Witten Theory
• A mathematical theory of quantum cohomology