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Twisted Sectors for Lagrangian Floer Theory on Symplectic Orbifolds

Bohui Chen, Kaoru Ono, Bai-Ling Wang

Abstract

The notion of twisted sectors play a crucial role in orbifold Gromov-Witten theory. We introduce the notion of dihedral twisted sectors in order to construct Lagrangian Floer theory on symplectic orbifolds and discuss related issues.

Twisted Sectors for Lagrangian Floer Theory on Symplectic Orbifolds

Abstract

The notion of twisted sectors play a crucial role in orbifold Gromov-Witten theory. We introduce the notion of dihedral twisted sectors in order to construct Lagrangian Floer theory on symplectic orbifolds and discuss related issues.
Paper Structure (9 sections, 1 theorem, 37 equations)

This paper contains 9 sections, 1 theorem, 37 equations.

Table of Contents

  1. Introduction
  2. The case of symplectic manifolds
  3. Orbifolds
  4. Presentation of an orbifold by a proper étale Lie groupoid
  5. Twisted sector and orbifold stable maps
  6. Lagrangian and dihedral twisted sector
  7. Definition of Lagrangians
  8. Dihedral twisted sector
  9. Filtered $\boldsymbol{A_{\infty}}$-structure associated with a Lagrangian

Key Result

Theorem 2.1

There is an isomorphism

Theorems & Definitions (7)

  • Theorem 2.1: FOOOantisymp
  • Definition 3.1
  • Definition 3.2
  • Definition 3.3
  • Definition 3.4
  • Definition 3.5
  • Definition 4.1