Title: HOMOLOGICAL MIRROR SYMMETRY AND TORUS FIBRATIONS
Abstract: Symplectic Geometry and Mirror Symmetry, pp. 203-263 (2001) No AccessHOMOLOGICAL MIRROR SYMMETRY AND TORUS FIBRATIONSMAXIM KONTSEVICH and YAN SOIBELMANMAXIM KONTSEVICHIHES, 35 route de Chartres, F-91440, France and YAN SOIBELMANDepartment of Mathematics, KSU, Manhattan, KS 66506, USAhttps://doi.org/10.1142/9789812799821_0007Cited by:114 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The following sections are included: Introduction Homological mirror symmetry and degenerations Content of the paper Degenerations of unitary Conformal Field Theories Moduli space of Conformal Field Theories Physical picture of a simple collapse Multiple collapse and the structure of the boundary Example: Toroidal models A-model and B-model of N = 2 SCFT as boundary strata Mirror symmetry and the collapse Calabi-Yau manifolds in the large complex structure limit Maximal degenerations of Calabi-Yau manifolds Monge-Ampère manifolds and duality of torus fibrations Speculations about relations with non-archimedean geometry A∞-algebras and A∞-categories Two problems with the general definition Non-unital A∞-algebras and A∞-categories A∞-pre-categories Example: directed A∞-pre-categories Fukaya category and its degeneration Fukaya category Fukaya-Oh category for torus fibration Morse-Smale complex and the category of Morse functions Notations from Morse theory Morse A∞-category of smooth functions De Rham A∞-category of smooth functions A∞-structure on a subcomplex Projectors and homotopies in Morse theory Proof of the theorem from 6.3 A∞-structure for the derived category of coherent sheaves Rigid analytic space A∞-structure on coherent sheaves Homological mirror conjecture Mirror symmetry functor on objects Spectrum of a morphism and the semigroup Homological mirror symmetry for abelian varieties Appendix: constructions in the case of complex numbers Mirror symmetry functor on objects over ℂ Sectors in the space of Dolbeault forms Semigroup φt References FiguresReferencesRelatedDetailsCited By 114Survey on the metric SYZ conjecture and non-Archimedean geometryYang Li19 July 2022 | International Journal of Modern Physics A, Vol. 37, No. 17The canonical wall structure and intrinsic mirror symmetryMark Gross and Bernd Siebert20 June 2022 | Inventiones mathematicae, Vol. 19Amplitudes in YM and GR as a Minimal Model and Recursive CharacterizationAndrea Nützi and Michael Reiterer7 April 2022 | Communications in Mathematical Physics, Vol. 392, No. 2Superfiltered A∞$A_\infty$‐deformations of the exterior algebra, and local mirror symmetryJack Smith10 March 2022 | Journal of the London Mathematical Society, Vol. 105, No. 4Homotopy Transfer and Effective Field Theory I: Tree‐levelAlex S. 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