ﻻ يوجد ملخص باللغة العربية
In this work we construct for a given smooth, generic Hamiltonian $H : mathbb{S}^1timesmathbb{T}^n longrightarrow mathbb{R}$ on the torus a chain isomorphism $ Phi_* : big(C_*(H),partial^M_*big) longrightarrow big(C_*(H),partial^F_*big)$ between the Morse complex of the Hamiltonian action $A_H$ on the free loop space of the torus $Lambda_0(mathbb{T}^n)$ and the Floer complex. Though both complexes are generated by the critical points of $A_H$, their boundary operators differ. Therefore the construction of $Phi$ is based on counting the moduli spaces of hybrid type solutions which involves stating a new non-Lagrangian boundary value problem for Cauchy-Riemann type operators not yet studied in Floer theory.
We analyze two different fibrations of a link complement M constructed by McMullen-Taubes, and studied further by Vidussi. These examples lead to inequivalent symplectic forms on a 4-manifold X = S x M, which can be distinguished by the dimension of
Fix a symplectic K3 surface X homologically mirror to an algebraic K3 surface Y by an equivalence taking a graded Lagrangian torus L in X to the skyscraper sheaf of a point y of Y. We show there are Lagrangian tori with vanishing Maslov class in X wh
We consider the Hamiltonian flow on complex complete intersection surfaces with isolated singularities, equipped with the Jacobian Poisson structure. More generally we consider complete intersections of arbitrary dimension equipped with Hamiltonian f
Given two $2n$--dimensional symplectic ellipsoids whose symplectic sizes satisfy certain inequalities, we show that a certain map from the $n$--torus to the space of symplectic embeddings from one ellipsoid to the other induces an injective map on si
In the spirit of recent work of Harada-Kaveh and Nishinou-Nohara-Ueda, we study the symplectic geometry of Popovs horospherical degenerations of complex algebraic varieties with the action of a complex linearly reductive group. We formulate an intrin