Rational Symplectic Field Theory for Legendrian knots

Abstract

We construct a combinatorial invariant of Legendrian knots in standard contact three-space. This invariant, which encodes rational relative Symplectic Field Theory and extends contact homology, counts holomorphic disks with an arbitrary number of positive punctures. The construction uses ideas from string topology.

58 pages, many figures; v3: minor corrections; final version, to appear in Inventiones Mathematicae

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• A Chekanov-Eliashberg algebra for Legendrian graphs
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