Heegaard Floer invariants of Legendrian knots in contact three-manifolds

Paolo Lisca; Peter Ozsváth; András I. Stipsicz; Zoltán Szabó

doi:10.4171/jems/183

Heegaard Floer invariants of Legendrian knots in contact three-manifolds

Paolo Lisca, Peter Ozsváth, András I. Stipsicz, Zoltán Szabó

Mathematics

Research output: Contribution to journal › Article › peer-review

54 Scopus citations

Abstract

We define invariants of null-homologous Legendrian and transverse knots in contact 3-manifolds. The invariants are determined by elements of the knot Floer homology of the underlying smooth knot. We compute these invariants, and show that they do not vanish for certain non-loose knots in overtwisted 3-spheres. Moreover, we apply the invariants to find transversely non-simple knot types in many overtwisted contact 3-manifolds.

Original language	English (US)
Pages (from-to)	1307-1363
Number of pages	57
Journal	Journal of the European Mathematical Society
Volume	11
Issue number	6
DOIs	https://doi.org/10.4171/jems/183
State	Published - 2009

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Keywords

Heegaard Floer homology
Legendrian knots
Transverse knots

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10.4171/jems/183

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abstract = "We define invariants of null-homologous Legendrian and transverse knots in contact 3-manifolds. The invariants are determined by elements of the knot Floer homology of the underlying smooth knot. We compute these invariants, and show that they do not vanish for certain non-loose knots in overtwisted 3-spheres. Moreover, we apply the invariants to find transversely non-simple knot types in many overtwisted contact 3-manifolds.",

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AU - Lisca, Paolo

AU - Ozsváth, Peter

AU - Stipsicz, András I.

AU - Szabó, Zoltán

PY - 2009

Y1 - 2009

N2 - We define invariants of null-homologous Legendrian and transverse knots in contact 3-manifolds. The invariants are determined by elements of the knot Floer homology of the underlying smooth knot. We compute these invariants, and show that they do not vanish for certain non-loose knots in overtwisted 3-spheres. Moreover, we apply the invariants to find transversely non-simple knot types in many overtwisted contact 3-manifolds.

AB - We define invariants of null-homologous Legendrian and transverse knots in contact 3-manifolds. The invariants are determined by elements of the knot Floer homology of the underlying smooth knot. We compute these invariants, and show that they do not vanish for certain non-loose knots in overtwisted 3-spheres. Moreover, we apply the invariants to find transversely non-simple knot types in many overtwisted contact 3-manifolds.

KW - Heegaard Floer homology

KW - Legendrian knots

KW - Transverse knots

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JF - Journal of the European Mathematical Society

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ER -

Heegaard Floer invariants of Legendrian knots in contact three-manifolds

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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