Related papers: On semi-global invariants for focus-focus singular…
In this note, we extend to the singular case some results on the birational geometry of irreducible holomorphic symplectic manifolds.
A singular riemannian foliation on a complete riemannian manifold is said to be riemannian if each geodesic that is perpendicular at one point to a leaf remains perpendicular to every leaf it meets. The singular foliation is said to admit…
We find a relation between Lagrangian Floer pairing of a symplectic manifold and Kapustin-Li pairing of the mirror Landau-Ginzburg model under localized mirror functor. They are conformally equivalent with an interesting conformal factor…
Submanifolds of a manifold are described as sections of a certain fiber bundle that enables one to consider their Lagrangian and (polysymplectic) Hamiltonian dynamics as that of a particular classical field theory. In particular, their…
In this paper we prove the connectedness of symplectic ball packings in the complement of a spherical Lagrangian, S^2 or RP^2, in symplectic manifolds that are rational or ruled. Via a symplectic cutting construction this is a natural…
Starting from a Heegaard splitting of a three-manifold, we use Lagrangian Floer homology to construct a three-manifold invariant, in the form of a relatively Z/8-graded abelian group. Our motivation is to have a well-defined symplectic side…
Since spectral invariants were introduced in cotangent bundles via generating functions by Viterbo in the seminal paper "Symplectic topology as the geometry of generating functions," they have been defined in various contexts, mainly via…
We explore the topology of real Lagrangian submanifolds in a toric symplectic manifold which come from involutive symmetries on its moment polytope. We establish a real analog of the Delzant construction for those real Lagrangians, which…
The graph of a real symplectic linear transformation is an R-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely imaginary and may be expressed in terms of the generating…
We introduce a holomorphic version of Weinstein's symplectic category, in which objects are holomorphic symplectic manifolds, and morphisms are holomorphic lagrangian correspondences. We then extend this category to log schemes, and prove…
In this paper we describe the cohomogeneity one special Lagrangian 3-folds in the cotangent bundle of the 3-sphere, also known in the physics literature as a deformed conifold. Our main result gives a global foliation of the deformed…
Quantization problems suggest that the category of symplectic manifolds and symplectomorphisms be augmented by the inclusion of canonical relations as morphisms. These relations compose well when a transversality condition is satisfied, but…
A singular real analytic foliation $\mathcal{F}$ of real codimension one on an $n$-dimensional complex manifold $M$ is Levi-flat if each of its leaves is foliated by immersed complex manifolds of dimension $n-1$. These complex manifolds are…
In this paper we classify all singular irreducible symplectic surfaces, i.e., compact, connected complex surfaces with canonical singularities that have a holomorphic symplectic form $\sigma$ on the smooth locus, and for which every finite…
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…
Suppose a Lagrangian is constructed from its fields and their derivatives. When the field configuration is a distribution, it is unambiguously defined as the limit of a sequence of smooth fields. The Lagrangian may or may not be a…
We study left-invariant foliations $\mathcal{F}$ on Riemannian Lie groups $G$ generated by a subgroup $K$. We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such foliations…
We classify solvable Lie groups admitting left invariant symplectic half-flat structure. When the Lie group has a compact quotient by a lattice, we show that these structures provide solutions of supersymmetric equations of type IIA.
We give a simple proof that, for a pre-quantized compact symplectic manifold with a Lagrangian torus fibration, its Riemann-Roch number coincides with its number of Bohr-Sommerfeld fibres. This can be viewed as an instance of the…
We define partial quasi-morphisms on the group of Hamiltonian diffeomorphisms of the cotangent bundle using the spectral invariants in Lagrangian Floer homology with conormal boundary conditions, where the product compatible with the PSS…