A combinatorial description of the Heegaard Floer contact invariant

Plamenevskaya, Olga

doi:10.2140/agt.2007.7.1201

Cited by 13 publications

(22 citation statements)

References 9 publications

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“…In our later arguments we will need the fact that the Heegaard diagram can be chosen to be strongly admissible, hence we address this issue presently, using an argument which was first used in [38]. Proposition 2.13.…”

Section: Contact Ozsváth-szabó Invariantsmentioning

confidence: 99%

Heegard Floer invariants of Legendrian knots in contact three-manifolds

Lisca¹,

Ozsváth²,

Stipsicz³

et al. 2009

J. Eur. Math. Soc.

205

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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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Section: Contact Ozsváth-szabó Invariantsmentioning

confidence: 99%

Heegard Floer invariants of Legendrian knots in contact three-manifolds

Lisca¹,

Ozsváth²,

Stipsicz³

et al. 2009

J. Eur. Math. Soc.

205

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“…In general we would need to apply finger moves and handle slides of the β curves in the Heegaard diagram. Handle slides, fortunately, do not arise in our case [15] and a finger move corresponds to a certain kind of isotopy of the β curves.…”

Section: Introductionmentioning

confidence: 75%

“…Therefore we know that the contact Ozsváth-Szabó invariant of ξ is nontrivial [13]. In the following we will verify this fact by the algorithm described in [15], but we will choose three different bases to illustrate that this choice is in fact crucial in calculations. 2.1.…”

Section: Remarkmentioning

confidence: 92%

On the contact Ozsváth-Szabó invariant

Etgü

Özbağcı

2010

Studia Scientiarum Mathematicarum Hungarica

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Sarkar and Wang proved that the hat version of Heegaard Floer homology group of a closed oriented 3-manifold is combinatorial starting from an arbitrary nice Heegaard diagram and in fact every closed oriented 3-manifold admits such a Heegaard diagram. Plamenevskaya showed that the contact Ozsváth-Szabó invariant is combinatorial once we are given an open book decomposition compatible with a contact structure. The idea is to combine the algorithm of Sarkar and Wang with the recent description of the contact Ozsváth-Szabó invariant due to Honda, Kazez and Matić. Here we simply observe that the hat version of the Heegaard Floer homology group and the contact Ozsváth-Szabó invariant in this group can be combinatorially calculated starting from a contact surgery diagram. We give detailed examples pointing out to some shortcuts in the computations.2000 Mathematics Subject Classification. 57R17, 57R65, 57R58, 57M99.

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“…The invariant c(ξ) can be calculated combinatorially as shown in [25] and [1]. However, for the present applications the usage of the c + is essential.…”

Section: Introductionmentioning

confidence: 99%

Contact structures on plumbed 3-manifolds

Karakurt¹

2014

Kyoto J. Math.

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Abstract. In this paper, we show that the Ozsváth-Szabó contact invariant c + (ξ) ∈ HF + (−Y ) of a contact 3-manifold (Y, ξ) can be calculated combinatorially if Y is the boundary of a certain type of plumbing X, and ξ is induced by a Stein structure on X. Our technique uses an algorithm of Ozsváth and Szabó to determine the Heegaard-Floer homology of such 3-manifolds. We discuss two important applications of this technique in contact topology. First, we show that it simplifies the calculation of the Ozsváth-StipsiczSzabó obstruction to admitting a planar open book. Then we define a numerical invariant of contact manifolds that respects a partial ordering induced by Stein cobordisms. We do a sample calculation showing that the invariant can get infinitely many distinct values.

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A combinatorial description of the Heegaard Floer contact invariant

Abstract: In this short note, we observe that the Heegaard Floer contact invariant is combinatorial by applying the algorithm of Sarkar--Wang to the description of the contact invariant due to Honda--Kazez--Matic. We include an example of this combinatorial calculation.Comment: 6 page

Cited by 13 publications

References 9 publications

Heegard Floer invariants of Legendrian knots in contact three-manifolds

Heegard Floer invariants of Legendrian knots in contact three-manifolds

On the contact Ozsváth-Szabó invariant

Contact structures on plumbed 3-manifolds

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