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Kuranishi Structures and Virtual Fundamental Chains /

The package of Gromov's pseudo-holomorphic curves is a major tool in global symplectic geometry and its applications, including mirror symmetry and Hamiltonian dynamics. The Kuranishi structure was introduced by two of the authors of the present volume in the mid-1990s to apply this machinery o...

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Bibliographic Details
Main Authors: Fukaya, Kenji (Author), Oh, Yong-Geun (Author), Ohta, Hiroshi (Author), Ono, Kaoru (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Singapore : Springer Singapore : Imprint: Springer, 2020.
Edition:1st ed. 2020.
Series:Springer Monographs in Mathematics,
Subjects:
Differential geometry.
Hyperbolic geometry.
Polytopes.
Differential Geometry.
Hyperbolic Geometry.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1.Introduction
  • 2.Notations and conventions
  • 3.Kuranishi structure and good coordinate system
  • 4.Fiber product of Kuranishi structures
  • 5.Thickening of a Kuranishi structure
  • 6.Multivalued perturbation
  • 7.CF-perturbation and integration along the fiber (pushout)
  • 8.Stokes' formula
  • 9.From good coordinate system to Kuranishi structure and back with CF-perturbations
  • 10.Composition formula of smooth correspondences
  • 11.Construction of good coordinate system
  • 12.Construction of CF-perturbations
  • 13.Construction of multivalued perturbations
  • 14.Zero and one dimensional cases via multivalued perturbation
  • 15.Introduction to Part 2
  • 16.Linear K-system: Floer cohomology I: statement
  • 17.Extension of Kuranishi structure and its perturbation from boundary to its neighborhood
  • 18.Smoothing corners and composition of morphisms
  • 19.Linear K-system: Floer cohomology II: proof
  • 20.Linear K-system: Floer cohomology III: Morse case by multisection
  • 21.Tree-like K-system: A1 structure I: statement
  • 22.Tree-like K-system: A1 structure II: proof
  • 23. Orbifold and orbibundle by local coordinate
  • 24.Covering space of effective orbifold and K-space
  • 25.Admissible Kuranishi structure
  • 26.Stratified submersion to a manifold with corners
  • 27.Local system and smooth correspondence in de Rham theory with twisted coefficients
  • 28.Composition of KG and GG embeddings: Proof of Lemma 3.34
  • 29.Global quotient and orbifold. .