2002/10/08 by Tobias Ekholm, Ekholm, Tobias, John Etnyre +3
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG
paper · pdf · doi:10.48550/arxiv.math/0210124
One example removed, minor updates to text
arxiv created 2002/12/05 · arxiv updated 2009/11/30
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.