NON-ISOTOPIC LEGENDRIAN SUBMANIFOLDS IN R2n+1
نویسندگان
چکیده
The contact homology, rigorously defined in [7], is computed for a number of Legendrian submanifolds in standard contact (2n+1)-space. The homology is used to detect infinite families of pairwise non-isotopic Legendrian n-spheres, n-tori, and surfaces which are indistinguishable using previously known invariants.
منابع مشابه
LEGENDRIAN SUBMANIFOLDS IN R2n+1 AND CONTACT HOMOLOGY
Contact homology for Legendrian submanifolds in standard contact (2n + 1)space is rigorously defined using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex n-space. The homology provides new invariants of Legendrian isotopy. These invariants show that the theory of Legendrian isotopy is very rich. For example, they detect infinite families of pairwise non-isotop...
متن کاملNon-isotopic Legendrian Submanifolds in R
In the standard contact (2n+1)-space when n > 1, we construct infinite families of pairwise non-Legendrian isotopic, Legendrian n-spheres, n-tori and surfaces which are indistinguishable using classically known invariants. When n is even these are the first known examples of non-Legendrian isotopic, Legendrian submanifolds of (2n + 1)-space. Such constructions indicate a rich theory of Legendri...
متن کاملTHE CONTACT HOMOLOGY OF LEGENDRIAN SUBMANIFOLDS IN R2n+1
We define the contact homology for Legendrian submanifolds in standard contact (2n + 1)-space using moduli spaces of holomorphic disks with Lagrangian boundary conditions in complex n-space. This homology provides new invariants of Legendrian isotopy which indicate that the theory of Legendrian isotopy is very rich. Indeed, in [4] the homology is used to detect infinite families of pairwise non...
متن کاملSecond Variation of Compact Minimal Legendrian Submanifolds of the Sphere
The second variation operator of minimal submanifolds of Riemannian manifolds (the Jacobi operator) carries information about stability properties of the submanifold when it is thought of as a critical point for the area functional. When the ambient Riemannian manifold is a sphere S, Simons [S] characterized the totally geodesic submanifolds as the minimal submanifolds of S either with the lowe...
متن کاملEquivariant Gluing Constructions of Contact Stationary Legendrian Submanifolds in S
A contact stationary Legendrian submanifold of S is a Legendrian submanifold whose volume is stationary under contact deformations. The simplest contact stationary Legendrian submanifold (actually minimal and Legendrian) is the real, equatorial n-sphere S0. This paper develops a method for constructing contact stationary (but not minimal) Legendrian submanifolds of S by gluing together configur...
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 2006