Dettaglio del documento
Lagrangian Floer theory and Its deformations : an introduction to filtered Fukaya category
Abstract
[...] The book starts with a quick explanation of Stasheff polytopes and their two realizations—one by the rooted metric ribbon trees and the other by the genus-zero moduli space of open Riemann surfaces—and an explanation of the A-infinity structure on the motivating example of the based loop space.
[...]
It then provides a description of the moduli space of genus-zero bordered stable maps and continues with the construction of the (curved) A-infinity structure and its canonical models. Included in the explanation are the (Landau–Ginzburg) potential functions associated with compact Lagrangian submanifolds constructed by Fukaya, Oh, Ohta, and Ono. The book explains calculations of potential functions for toric fibers in detail and reviews several explicit calculations in the literature of potential functions with bulk as well as their applications to problems in symplectic topology via the critical point theory thereof. In the Appendix, the book also provides rapid summaries of various background materials such as the stable map topology, Kuranishi structures, and orbifold Lagrangian Floer theory. (Estratto dal sito dell'editore)
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| eBook | ||
| Monografia | ||
| Description | *Lagrangian Floer theory and Its deformations : an introduction to filtered Fukaya category / Yong-Geun Oh. - Singapore : Springer, 2024. - 1 testo elettronico (xvii, 416 p. : ill.) | |
| ISBN E-Book | 9789819717989 | |
| Series | KIAS Springer Series in Mathematics , 2 | |
| Author |
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| Subjects | 53D37 - Mirror symmetry, symplectic aspects; homological mirror symmetry and Fukaya category [MSC 2020] | |
| 53D40 - Symplectic aspects of Floer homology and cohomology [MSC 2020] | ||
| 57R58 - Floer homology [MSC 2020] | ||
| Parole chiave |
A Infinity Structure
Fukaya category Hochschild Complex Lagrangian submanifolds Moduli Space of Pseudoholomorphic Discs |
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| Publication place | Singapore | |
| Publisher | Springer <editore> | |
| Publication year | 2024 | |
| Thesaurus | 53D37 | |
| 53D40 | ||
| 57R58 | ||
| Floer homology [MSC 2020] | ||
| Mirror symmetry, symplectic aspects; homological mirror symmetry and Fukaya category [MSC 2020] | ||
| Symplectic aspects of Floer homology and cohomology [MSC 2020] |