Non-isotopic Legendrian submanifolds in R2n+1
نویسندگان
چکیده
منابع مشابه
NON-ISOTOPIC LEGENDRIAN SUBMANIFOLDS IN R2n+1
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.
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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...
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We show that there is no positive loop inside the component of a fiber in the space of Legendrian embeddings in the contact manifold ST ∗M , provided that the universal cover of M is Rn. We consider some related results in the space of one-jets of functions on a compact manifold. We give an application to the positive isotopies in homogeneous neighborhoods of surfaces in a tight contact 3-manif...
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 کاملLEGENDRIAN 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...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 2005
ISSN: 0022-040X
DOI: 10.4310/jdg/1143644313