Explicit expressions for the Iwasawa factors, the metric and the monodromy matrices for minimal Lagrangian surfaces in $\mathbb{C} P^2$

同调 Lagrangian 单值性与 Wang 正合序列

Homological Lagrangian monodromy and Wang exact sequence

该研究利用能量阈值条件证明 Lagrangian 子流形的同调单值性在无低能 J-全纯球面或圆盘时为平凡。

Homological Lagrangian monodromy

We show that the Hamiltonian Lagrangian monodromy group, in its homological version, is trivial for any weakly exact Lagrangian submanifold of a symplectic manifold. The proof relies on a sheaf approach to Floer homology given by a relative Seidel morphism.

Generalized special Lagrangian torus fibration for Calabi-Yau hypersurfaces in toric varieties II

In this paper we construct monodromy representing generalized special Lagrangian torus fibrations for Calabi-Yau hypersurfaces in toric varieties near the large complex limit.

Moment maps, monodromy and mirror manifolds

Via considerations of symplectic reduction, monodromy, mirror symmetry and Chern-Simons functionals, a conjecture is proposed on the existence of special Lagrangians in the hamiltonian deformation class of a given Lagrangian submanifold of a Calabi-Yau manifold. It involves a stability condition for graded Lagrangians, and can be proved for the simple case of $T^2$.

Symplectic monodromy, Leray residues and quasi-homogeneous polynomials

We formulate certain sufficient conditions for the symplectic monodromy of an isolated quasihomogeneous singularity to be of infinite order in the relative symplectic mapping class group of the Milnor fibre and give a proof using Maslov classes, stability theory for Lagrangian folds resp. stable Morse theory for generating families as well as algebraic results about relative cohomology of smoothings of isolated singularities. Our conditions being slightly more restrictive than Seidel's, in contrary to Seidel's proof, we do not use Floer theory to derive this result. An alternative approach usi…

P=W for Lagrangian fibrations and degenerations of hyper-Kähler manifolds

We identify the perverse filtration of a Lagrangian fibration with the monodromy weight filtration of a maximally unipotent degeneration of compact hyper-Kähler manifolds.