相关论文: Graded Lagrangian submanifolds

According to the Arnold conjectures and Floer's proofs, there are non-trivial lower bounds for the number of periodic solutions of Hamiltonian differential equations on a closed symplectic manifold whose symplectic form vanishes on spheres.…

We define an integer graded symplectic Floer cohomology and a Fintushel-Stern type spectral sequence which are new invariants for monotone Lagrangian sub-manifolds and exact isotopes. The Z-graded symplectic Floer cohomology is an integral…

The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analogue for an isolated singularity. We define the monodromy Lagrangian Floer…

We define additional gradings on two generalisations of Khovanov homology (one due to the first author, the other due to the second), and use them to define invariants of various kinds of embeddings. These include invariants of links in…

We classify holomorphic isometric actions on complex space forms all whose orbits are Lagrangian submanifolds, up to orbit equivalence. The only examples are Lagrangian affine subspace foliations of complex Euclidean spaces, and Lagrangian…

A previous result about the decategorified bordered (sutured) Heegaard Floer invariants of surfaces glued together along intervals, generalizing the decategorified content of Rouquier and the author's higher-tensor-product-based gluing…

Butscher, D. Lee, Y. Lee, and Joyce constructed a special Lagrangian submanifold by gluing a Lawlor neck into a transverse intersection point of two special Lagrangian submanifolds. We prove a uniqueness theorem for the gluing of flat…

The special geometry of calibrated cycles, closely related to mirror symmetry among Calabi--Yau 3-folds, is itself a real form of a new subject, which we call slightly deformed algebraic geometry. On the other hand, both of these geometries…

In an earlier paper (math.SG/0110169), we introduced absolute gradings on the three-manifold invariants developed in math.SG/0101206 and math.SG/0105202. Coupled with the surgery long exact sequences, we obtain a number of three- and…

We study a class of 3-manifolds called strong L-spaces, which by definition admit a certain type of Heegaard diagram that is particularly simple from the perspective of Heegaard Floer homology. We provide evidence for the possibility that…

`Gluing' is a technique of constructing solutions to non-linear (elliptic) partial differential equations such as Yang--Mills equations, minimal surface equations and Einstein equations. Calibrated submanifolds are a certain class of…

The main theorem of this paper asserts that the inclusion of the space of projective Lagrangian planes into the space of Lagrangian submanifolds of complex projective space induces an injective homomorphism of fundamental groups. We…

For a subvariety of a smooth projective variety, consider the family of smooth hypersurfaces of sufficiently large degree containing it, and take the quotient of the middle cohomology of the hypersurfaces by the cohomology of the ambient…

For any irreducible compact homogeneous K\"ahler manifold, we classify the compact tight Lagrangian submanifolds which have the Z_2-homology of a sphere.

In this article we obtain a classification of special Lagrangian submanifolds in complex space forms subject to an $SO(2)\rtimes S_3$-symmetry on the second fundamental form. The algebraic structure of this form has been obtained by…

We define an simple invariant of an embedded nullhomologous Lagrangian torus and use this invariant to show that many symplectic 4-manifolds have infinitely many pairwise symplectically inequivalent nullhomologous Lagrangian tori. We…

We study lagrangian submanifolds of algebraic variety Gr(1, n) equipped with the Kahler form given by the Plucker embedding. We use the correspondence between lagrangian submanifolds of Gr(1, n) and lagrangian submanifolds of variety…

We study Lagrangian cobordism groups of closed symplectic surfaces of genus $g \geq 2$ whose relations are given by unobstructed, immersed Lagrangian cobordisms. Building upon work of Abouzaid and Perrier, we compute these cobordism groups…

In this article we describe an algebraic framework which can be used in three related but different contexts: string topology, symplectic field theory, and Lagrangian Floer theory of higher genus. It turns out that the relevant algebraic…

This is the fourth in a series of papers math.DG/0008021, math.DG/0008155, math.DG/0010036 constructing explicit examples of special Lagrangian submanifolds (SL m-folds) in C^m. A submanifold of C^m is ruled if it is fibred by a family of…