Disjoinable Lagrangian Spheres and Dilations
نویسنده
چکیده
We consider open symplectic manifolds which admit dilations (in the sense previously introduced by Solomon and the author). We obtain restrictions on collections of Lagrangian submanifolds which are pairwise disjoint (or pairwise disjoinable by Hamiltonian isotopies) inside such manifolds. This includes the Milnor fibres of isolated hypersurface singularities which have been stabilized (by adding quadratic terms) sufficiently often.
منابع مشابه
Lagrangian unknottedness in Stein surfaces
We show that the space of Lagrangian spheres inside the cotangent bundle of the 2-sphere is contractible. We then discuss the phenomenon of Lagrangian unknottedness in other Stein surfaces. There exist homotopic Lagrangian spheres which are not Hamiltonian isotopic, but we show that in a typical case all such spheres are still equivalent under a symplectomorphism.
متن کاملLagrangian spheres, symplectic surfaces and the symplectic mapping class group
Given a Lagrangian sphere in a symplectic 4-manifold (M,ω) with b+ = 1, we find embedded symplectic surfaces intersecting it minimally. When the Kodaira dimension κ of (M,ω) is −∞, this minimal intersection property turns out to be very powerful for both the uniqueness and existence problems of Lagrangian spheres. On the uniqueness side, for a symplectic rational manifold and any class which is...
متن کاملOn Hamiltonian Stationary Lagrangian Spheres in Non-einstein Kähler Surfaces
Hamiltonian stationary Lagrangian spheres in Kähler-Einstein surfaces are minimal. We prove that in the family of non-Einstein Kähler surfaces given by the product Σ1×Σ2 of two complete orientable Riemannian surfaces of different constant Gauss curvatures, there is only a (non minimal) Hamiltonian stationary Lagrangian sphere. This example is defined when the surfaces Σ1 and Σ2 are spheres.
متن کاملLagrangian Spheres in Del Pezzo Surfaces
Lagrangian spheres in the symplectic Del Pezzo surfaces arising as blow-ups of CP in 4 or fewer points are classified up to Lagrangian isotopy. Unlike the case of the 5-point blow-up, there is no Lagrangian knotting.
متن کاملComplex Extensors and Lagrangian Submanifolds in Complex Euclidean Spaces
Lagrangian //-umbilical submanifolds are the "simplest" Lagrangian submanifolds next to totally geodesic ones in complex-space-forms. The class of Lagrangian //-umbilical submanifolds in complex Euclidean spaces includes Whitney's spheres and Lagrangian pseudo-spheres. For each submanifold M of Euclidean «-space and each unit speed curve F in the complex plane, we introduce the notion of the co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013