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Table of Contents
Cover
Title page
Chapter 1. Introduction
Chapter 2. A-infinity algebra over a noncommutative base
2.1. Review of filtered A-infinity category and weak Maurer-Cartan elements
2.2. \AI-functors and Yoneda embedding
2.3. \AI-algebra over a noncommutative base and weakly unobstructedness
Chapter 3. Noncommutative mirror from a single Lagrangian and the centrality theorem
3.1. Noncommutative family of Maurer-Cartan elements
3.2. Noncommutative mirrors using a single immersed Lagrangian
3.3. Spacetime superpotential and Maurer-Cartan equation
3.4. Centrality
Chapter 4. The mirror functor from a single Lagrangian
Chapter 5. Elliptic curves and deformation quantizations
5.1. Deforming the reference Lagrangian
5.2. Sklyanin algebras as Weak Maurer-Cartan relations
5.3. Noncommutative potential
5.4. ( , , ) and the mirror elliptic curve
5.5. Relation to the quantization of an affine del Pezzo surface
Chapter 6. Mirror construction using several Lagrangians and quiver algebras
6.1. Path algebra and the semi-simple ring
6.2. Mirror construction
6.3. Centrality and the spacetime superpotential
6.4. The mirror functor
Chapter 7. Finite group symmetry and graded mirror functors
7.1. Kähler manifolds with finite group symmetry
7.2. Calabi-Yau manifolds with finite-group symmetry
Chapter 8. 4-punctured spheres and the pillowcase
8.1. Mirror of the four-punctured sphere
8.2. Mirror of the pillowcase
8.3. Open mirror theorem
8.4. Deformation of the reference Lagrangian \bL
8.5. Relation to the quantization of an intersection of two quadrics in \C⁴
Chapter 9. Extended mirror functor
9.1. Extended Landau-Ginzburg mirror
9.2. Extended mirror functor
Chapter 10. Mirror construction for punctured Riemann surface.
10.1. Reference Lagrangian from a polygonal decomposition
10.2. Floer theory for \bL and its Maurer-Cartan space for a dimer
10.3. Relation to the mirror dimer model ^{∨}
10.4. The case of a non-dimer
10.5. Perfect matching and \Z-grading
10.6. Mirror functor
Chapter 11. Mirrors of Calabi-Yau threefolds associated with quadratic differentials
11.1. Non-compact Calabi-Yau threefolds associated with quadratic differentials
11.2. Generalized mirrors
11.3. Mirror functor
Appendix A. Theta function calculations
A.1. Weak Maurer-Cartan relations for ℙ¹_{3,3,3}
A.2. Weak Maurer-Cartan relations for ℙ¹_{2,2,2,2}
A.3. Embedding of _{ } into ℙ³
Bibliography
Back Cover.
Title page
Chapter 1. Introduction
Chapter 2. A-infinity algebra over a noncommutative base
2.1. Review of filtered A-infinity category and weak Maurer-Cartan elements
2.2. \AI-functors and Yoneda embedding
2.3. \AI-algebra over a noncommutative base and weakly unobstructedness
Chapter 3. Noncommutative mirror from a single Lagrangian and the centrality theorem
3.1. Noncommutative family of Maurer-Cartan elements
3.2. Noncommutative mirrors using a single immersed Lagrangian
3.3. Spacetime superpotential and Maurer-Cartan equation
3.4. Centrality
Chapter 4. The mirror functor from a single Lagrangian
Chapter 5. Elliptic curves and deformation quantizations
5.1. Deforming the reference Lagrangian
5.2. Sklyanin algebras as Weak Maurer-Cartan relations
5.3. Noncommutative potential
5.4. ( , , ) and the mirror elliptic curve
5.5. Relation to the quantization of an affine del Pezzo surface
Chapter 6. Mirror construction using several Lagrangians and quiver algebras
6.1. Path algebra and the semi-simple ring
6.2. Mirror construction
6.3. Centrality and the spacetime superpotential
6.4. The mirror functor
Chapter 7. Finite group symmetry and graded mirror functors
7.1. Kähler manifolds with finite group symmetry
7.2. Calabi-Yau manifolds with finite-group symmetry
Chapter 8. 4-punctured spheres and the pillowcase
8.1. Mirror of the four-punctured sphere
8.2. Mirror of the pillowcase
8.3. Open mirror theorem
8.4. Deformation of the reference Lagrangian \bL
8.5. Relation to the quantization of an intersection of two quadrics in \C⁴
Chapter 9. Extended mirror functor
9.1. Extended Landau-Ginzburg mirror
9.2. Extended mirror functor
Chapter 10. Mirror construction for punctured Riemann surface.
10.1. Reference Lagrangian from a polygonal decomposition
10.2. Floer theory for \bL and its Maurer-Cartan space for a dimer
10.3. Relation to the mirror dimer model ^{∨}
10.4. The case of a non-dimer
10.5. Perfect matching and \Z-grading
10.6. Mirror functor
Chapter 11. Mirrors of Calabi-Yau threefolds associated with quadratic differentials
11.1. Non-compact Calabi-Yau threefolds associated with quadratic differentials
11.2. Generalized mirrors
11.3. Mirror functor
Appendix A. Theta function calculations
A.1. Weak Maurer-Cartan relations for ℙ¹_{3,3,3}
A.2. Weak Maurer-Cartan relations for ℙ¹_{2,2,2,2}
A.3. Embedding of _{ } into ℙ³
Bibliography
Back Cover.