On invariants for Legendrian knots
arXiv:0806.1436
Abstract
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.
19 pages, 11 figures
References in corpus (6)
- Floer homology and knot complements
- Contact structures, sutured Floer homology and TQFT
- The vanishing of the contact invariant in the presence of torsion
- Heegaard Floer invariants of Legendrian knots in contact three--manifolds
- Giroux torsion and twisted coefficients
- Topologically Trivial Legendrian Knots