Fukaya categories of two-tori revisited
نویسندگان
چکیده
We construct an A?-structure of the Fukaya category explicitly for any flat symplectic two-torus. The structure constants non-transversal A?-products are obtained as derivatives those transversal A?-products.
منابع مشابه
Fukaya categories and deformations
Soon after their first appearance [7], Fukaya categories were brought to the attention of a wider audience through the homological mirror conjecture [14]. Since then Fukaya and his collaborators have undertaken the vast project of laying down the foundations, and as a result a fully general definition is available [9, 6]. The task that symplectic geometers are now facing is to make these catego...
متن کاملFukaya Categories as Categorical Morse Homology
The Fukaya category of a Weinstein manifold is an intricate symplectic invariant of high interest in mirror symmetry and geometric representation theory. This paper informally sketches how, in analogy with Morse homology, the Fukaya category might result from gluing together Fukaya categories of Weinstein cells. This can be formalized by a recollement pattern for Lagrangian branes parallel to t...
متن کاملA Topological Model for the Fukaya Categories of Plumbings
We prove that the algebra of singular cochains on a smooth manifold, equipped with the cup product, is equivalent to the A∞ structure on the Lagrangian Floer cochain group associated to the zero section in the cotangent bundle. More generally, given a pair of smooth manifolds Q1 and Q2 of the same dimension with embeddings of a submanifold B with isomorphic normal bundles, we construct a differ...
متن کاملFukaya categories of the torus and Dehn surgery.
This paper is a companion to the authors' forthcoming work extending Heegaard Floer theory from closed 3-manifolds to compact 3-manifolds with two boundary components via quilted Floer cohomology. We describe the first interesting case of this theory: the invariants of 3-manifolds bounding S(2) [symbol: see text] T(2), regarded as modules over the Fukaya category of the punctured 2-torus. We ex...
متن کاملThree Lectures on Fukaya-Seidel Categories and Web-Based Formalism
Lecture notes for three lectures in Florida, Jan. 26-29, 2015. These lectures describe some aspects of a forthcoming paper with D. Gaiotto and E. Witten, Version: January 29, 2015
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2021
ISSN: ['1879-1662', '0393-0440']
DOI: https://doi.org/10.1016/j.geomphys.2020.103965