UID:
almahu_9949926883802882
Format:
1 online resource (128 pages)
Edition:
1st ed.
ISBN:
9781470466305
Series Statement:
Memoirs of the American Mathematical Society Series ; v.271
Note:
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.
Additional Edition:
Print version: Cho, Cheol-Hyun Noncommutative Homological Mirror Functor Providence : American Mathematical Society,c2021 ISBN 9781470447618
Language:
English
Keywords:
Electronic books.
