The Contact Homology of Legendrian Submanifolds in $\R^{2n+1}$
Joint work with Tobias Ekholm and Michael G. Sullivan,
J. Differential Geom. 71 (2005), no. 2, 177-305.

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 Non-isotopic Legendrian Submanifolds in $\R^{2n+1}$ the homology is used to detect infinite families of pairwise non-isotopic Legendrian submanifolds which are indistinguishable using previously known invariants.

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