A bound for rational Thurston–Bennequin invariants

Li, Youlin; Wu, Zhongtao

doi:10.1007/s10711-018-0377-7

Cited by 5 publications

(4 citation statements)

References 20 publications

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“…see [42,Lemma 4.1]. It follows from this and from Theorem 2.8 that we can get a lower bound on the number of distinct tight contact structures by counting the number of possible values of rot Q of each L i .…”

Section: Proposition 43mentioning

confidence: 91%

Classification of tight contact structures on surgeries on the figure-eight knot

Conway,

Min

2019

Preprint

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Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. We present the first such classification on an infinite family of (mostly) hyperbolic 3-manifolds: surgeries on the figure-eight knot. We also determine which of the tight contact structures are symplectically fillable and which are universally tight.

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Section: Proposition 43mentioning

confidence: 91%

Classification of tight contact structures on surgeries on the figure-eight knot

Conway,

Min

2019

Preprint

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“…Thus τ ξ (Y, K) may be a rational number. See [17] or [14] for more details. In [13], the authors prove an analogue of (2) which constrains the genera of cobordisms between cables of rationally null-homologous knots.…”

Section: Proof By LI and Wumentioning

confidence: 99%

4-dimensional aspects of tight contact 3-manifolds

Hedden,

Raoux

2020

Preprint

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In this article we conjecture a 4-dimensional characterization of tightness: a contact structure on a 3-manifold Y is tight if and only if a slice-Bennequin inequality holds for smoothly embedded surfaces in Y × [0, 1]. An affirmative answer to our conjecture would imply an analogue of the Milnor conjecture for torus knots: if a fibered link L induces a tight contact structure on Y then its fiber surface maximize Euler characteristic amongst all surfaces in Y ×[0, 1] with boundary L. We provide evidence for both conjectures by proving them for contact structures with non-vanishing Ozsváth-Szabó contact invariant.

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“…The last two authors introduced an invariant τ * c(ξ) (Y, K) for a rationally null-homologous knot K in a contact 3-manifold (Y, ξ) with non-vanishing contact invariant c(ξ) [25], and proved that this invariant gives an upper bound for the sum of the rational Thurston-Bennequin invariant and the absolute value of the rational rotation number of all Legendrian knots isotopic to K, i.e.…”

Section: Introductionmentioning

confidence: 99%

Contact $(+1)$-surgeries on rational homology $3$-spheres

Fan

2022

Journal of Symplectic Geometry

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In this paper, sufficient conditions for contact (+1)-surgeries along Legendrian knots in contact rational homology 3-spheres to have vanishing contact invariants or to be overtwisted are given. They can be applied to study contact (±1)-surgeries along Legendrian links in the standard contact 3-sphere. We also obtain a sufficient condition for contact (+1)-surgeries along Legendrian twocomponent links in the standard contact 3-sphere to be overtwisted via their front projections.

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A bound for rational Thurston–Bennequin invariants

Cited by 5 publications

References 20 publications

Classification of tight contact structures on surgeries on the figure-eight knot

Classification of tight contact structures on surgeries on the figure-eight knot

4-dimensional aspects of tight contact 3-manifolds

Contact $(+1)$-surgeries on rational homology $3$-spheres

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