Colloquium

Colloquium
On Hamiltonian deformation of loops 薮義郎 12月8日(金) 13時30分 A problem we consider in the talk is when two embedded loops in a symplectic manifold are deformed into each other by a Hamiltonian flow. An answer for it is given in the case that the dimension of a symplectic manifold is greater than two. In a two-dimensional case, this problem is concerned with the Lagrangian intersection theory, where hard analysis is required, for instance, pseudo-holomorphic curves and Floer (co)homology. By making use of holomorphic curves, we discuss an existence of a Hamiltonian isotopy between two loops in an oriented surface.

On Hamiltonian deformation of loops

薮義郎

12月8日(金) 13時30分

A problem we consider in the talk is when two embedded loops in a symplectic manifold are deformed into each other by a Hamiltonian flow. An answer for it is given in the case that the dimension of a symplectic manifold is greater than two. In a two-dimensional case, this problem is concerned with the Lagrangian intersection theory, where hard analysis is required, for instance, pseudo-holomorphic curves and Floer (co)homology. By making use of holomorphic curves, we discuss an existence of a Hamiltonian isotopy between two loops in an oriented surface.