LEGENDRIAN SUBMANIFOLDS IN R2n+1 AND CONTACT HOMOLOGY
نویسندگان
چکیده
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-isotopic Legendrian n-spheres, n-tori, and surfaces which are indistinguishable using previously known invariants. In a sense, the definition of contact homology presented in this paper is a high dimensional analog of the work of Chekanov and others on Legendrian 1-knots in 3-space.
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