Hofer's diameter and Lagrangian intersections

Diameters of Ball Intersections

We prove the diameter of the intersection of two closed convex balls in a Riemannian manifold eventually decreases continuously as the centers of the balls move apart.

拉格朗日相交与Arnol'd的一个猜想

Lagrangian intersections and a conjecture of Arnol'd

该研究提出新版本拉格朗日Ljusternik–Schnirelman理论，证明了Floer与Hofer研究之外的退化同调Arnol'd猜想，引入基本量子分解给出经典例子的拉格朗日相交数下界，并研究了单调拉格朗日与其哈密顿微分同胚像的相交规模。

辛微分同胚群的几何

A translation of "The Geometry of the Group of Symplectic Diffeomorphisms"

本书介绍霍费尔度量，研究哈密顿微分同胚群的直径、测地线及单参数子群增长，并应用于动力学和遍历理论。

Lagrangian Intersections and the Serre Spectral Sequence

For a transversal pair of closed Lagrangian submanifolds L, L' of a symplectic manifold M so that $π_{1}(L)=π_{1}(L')=0=c_{1}|_{π_{2}(M)}=ω|_{π_{2}(M)}$ and a generic almost complex structure J we construct an invariant with a high homotopical content which consists in the pages of order $\geq 2$ of a spectral sequence whose differentials provide an algebraic measure of the high-dimensional moduli spaces of pseudo-holomorpic strips of finite energy that join L and L'. When L and L' are hamiltonian isotopic, these pages coincide (up to a horizontal translation) with the terms of the Serre-spect…