Squeezing in Floer theory and refined Hofer–Zehnder capacities of sets near symplectic submanifolds
نویسندگان
چکیده
منابع مشابه
Squeezing in Floer theory and refined Hofer–Zehnder capacities of sets near symplectic submanifolds
We use Floer homology to study the Hofer–Zehnder capacity of neighborhoods near a closed symplectic submanifold M of a geometrically bounded and symplectically aspherical ambient manifold. We prove that, when the unit normal bundle of M is homologically trivial in degree dim(M) (for example, if codim(M) > dim(M)), a refined version of the Hofer–Zehnder capacity is finite for all open sets close...
متن کاملPeriodic Orbits near Symplectic Submanifolds
We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has nonvanishing symplectic homology. As a consequence, we establish the existence of contractible closed characteristics on any thickening of the boundary of the neighborhood. When applied to twisted geodesic flows on compact symplectically aspherical manifolds, this i...
متن کاملDevelopment in symplectic Floer theory
In the middle of the 1980s, Floer initiated a new theory, which is now called the Floer theory. Since then the theory has been developed in various ways. In this article we report some recent progress in Floer theory in symplectic geometry. For example, we give an outline of a proof of the flux conjecture, which states that the Hamiltonian diffeomorphism group is C1-closed in the group of sympl...
متن کاملSymplectic Homology and Periodic Orbits near Symplectic Submanifolds
We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has nonvanishing symplectic homology. As a consequence, we establish the existence of contractible closed characteristics on any thickening of the boundary of the neighborhood. When applied to twisted geodesic flows on compact symplectically aspherical manifolds, this i...
متن کاملPeriodic Orbits of Hamiltonian Flows near Symplectic Critical Submanifolds
In this paper we produce a lower bound for the number of periodic orbits of certain Hamiltonian vector fields near Bott-nondegenerate symplectic critical submanifolds. This result is then related to the problem of finding closed orbits of the motion of a charged low energy particle on a Riemannian manifold under the influence of a magnetic field.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Geometry & Topology
سال: 2005
ISSN: 1364-0380,1465-3060
DOI: 10.2140/gt.2005.9.1775