On invariants for Legendrian knots

A. Stipsicz, Vera Vértesi

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Let (Y, ξ) be a contact 3-manifold and L a null-homologous Legendrian knot in it. We determine the connection between the sutured invariant EH(L) = EH(Y - ν(L), ξ|Y - ν(L)) of L and the Legendrian invariant ℒ(L) defined in a paper by Lisca, Ozsváth, Stipsicz and Szabó. We derive a vanishing theorem for ℒ(L) in the presence of Giroux torsion in the complement of the knot, and reprove several known properties of the Legendrian invariant from this perspective.

Original languageEnglish
Pages (from-to)157-177
Number of pages21
JournalPacific Journal of Mathematics
Volume239
Issue number1
DOIs
Publication statusPublished - Jan 2009

Fingerprint

Legendrian Knot
Invariant
Vanishing Theorems
Knot
Torsion
Null
Complement
Contact

Keywords

  • Heegaard Floer homology
  • Legendrian and transverse knot
  • Sutured Floer homology

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On invariants for Legendrian knots. / Stipsicz, A.; Vértesi, Vera.

In: Pacific Journal of Mathematics, Vol. 239, No. 1, 01.2009, p. 157-177.

Research output: Contribution to journalArticle

Stipsicz, A. ; Vértesi, Vera. / On invariants for Legendrian knots. In: Pacific Journal of Mathematics. 2009 ; Vol. 239, No. 1. pp. 157-177.
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