Legendrian Submanifolds in $R^{2n+1}$ and Contact Homology

Details Legendrian Submanifolds in $R^{2n+1}$ and Contact Homology Legendrian Submanifolds in $R^{2n+1}$ and Contact Homology

2002-10-08

arxiv.org/abs/math/0210124v3

Mathematics

Symplectic Geometry

One example removed, minor updates to text

Scientific paper

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. It provides new invariants of Legendrian isotopy. Using these invariants the theory of Legendrian isotopy is shown to be very rich. For example, infinite families of pairwise non-isotopic Legendrian $n$-spheres and $n$-tori, which are indistinguishable by means of previously known invariants, are constructed. 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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