On invariants for Legendrian knots

Details On invariants for Legendrian knots On invariants for Legendrian knots

2008-06-09

arxiv.org/abs/0806.1436v2

Mathematics

Symplectic Geometry

19 pages, 11 figures

Scientific paper

Suppose that L is a null--homologous Legendrian knot in a contact 3--manifold. We determine the connection between the sutured invariant of the complement of L and the Legendrian invariant defined by Lisca, Ozsvath, Stipsicz and Szabo. In particular, we derive a vanishing theorem for the Legendrian invariant in the presence of Giroux torsion in the complement of the knot, and reprove several known properties of the Legendrian invariant from this perspective.

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