Related papers: Fukaya's work on Lagrangian embeddings
In the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both open and closed strings. We show that these terms naturally fit into a 2-dimensional, smooth…
In this paper, we prove various results on the topology of the Grassmannian of oriented 3-planes in Euclidean 6-space and compute its cohomology ring. We give self-contained proofs. These spaces come up when studying submanifolds of…
We define topological invariants of regular Lagrangian fibrations using the integral affine structure on the base space and we show that these coincide with the classes known in the literature. We also classify all symplectic types of…
Let (M,w) be a compact symplectic manifold, and L a compact, embedded Lagrangian submanifold in M. Fukaya, Oh, Ohta and Ono construct Lagrangian Floer cohomology for such M,L, yielding groups HF^*(L,b;\Lambda) for one Lagrangian or…
I start with a scenario where the universe is an abstract space $\mathcal{M}$ having $d$ dimensions. There is a two dimensional surface embedded in it. Embedding is a map from the embedded surface to $\mathcal{M}$ that has a field theory…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
Motivated by work of the first author, this paper studies symplectic embedding problems of lagrangian products that are sufficiently symmetric. In general, lagrangian products arise naturally in the study of billiards. The main result of…
In the usual setup, the grading on Floer homology is relative: it is unique only up to adding a constant. "Graded Lagrangian submanifolds" are Lagrangian submanifolds with a bit of extra structure, which fixes the ambiguity in the grading.…
The paper discusses some aspects of Gromov's theory.
We show how topological open string theory amplitudes can be computed by using relative stable morphisms in the algebraic category. We achieve our goal by explicitly working through an example which has been previously considered by Ooguri…
In this short note we discuss high-dimensional examples of Legendrian submanifolds of the standard contact Euclidean space with an infinite number of exact Lagrangian fillings up to Hamiltonian isotopy. They are obtained from the examples…
The 2016 papers of J. Solomon and S. Tukachinsky use bounding chains in Fukaya's $A_{\infty}$-algebras to define numerical disk counts relative to a Lagrangian under certain regularity assumptions on the moduli spaces of disks. We present a…
This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for fermions on Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded…
This short and fairly informal note is an attempt to explain how methods of homological algebra may be brought to bear on problems in symplectic geometry. We do this by looking at a familiar sample question, which is that of the topology of…
The main theme of this paper is the introduction of a new type of polarizations, suited for some open symplectic manifolds, and their applications. These applications include symplectic embedding results that answer a question by…
We extend constructions and results of Damian to get topological obstructions to the existence of closed monotone Lagrangian embeddings into the cotangent bundle of a space which is the total space of a fibration over the circle.
This paper is devoted to study gauge embedding of either commutative and noncommutative theories in the framework of the symplectic formalism. We illustrate our ideas in the Proca model, the irrotational fluid model and the noncommutative…
I point out that (BPS saturated) A-type D-branes in superstring compactifications on Calabi-Yau threefolds correspond to {\em graded} special Lagrangian submanifolds, a particular case of the graded Lagrangian submanifolds considered by M.…
In this paper, we study a family of symplectic manifolds introduced by Woodward. These manifolds belong to the broader class of \emph{multiplicity-free} Hamiltonian $G$-manifolds, a generalization of toric manifolds for non-abelian…
This (partially expository) paper discusses Lagrangian Floer cohomology in the context of Lefschetz fibrations, with emphasis on the algebraic structures encountered there. In addition to the well-known directed A_infinity algebras which…