Rational Symplectic Field Theory for Legendrian knots

Details Rational Symplectic Field Theory for Legendrian knots Rational Symplectic Field Theory for Legendrian knots

2008-06-27

arxiv.org/abs/0806.4598v3

Invent. Math. 182 (2010), no. 3, 451--512

Mathematics

Symplectic Geometry

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

Scientific paper

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.

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