Symplectic Fillings, Contact Surgeries, and Lagrangian Disks

Conway, James; Etnyre, John B.; Tosun, Bülent

doi:10.1093/imrn/rny291

Cited by 18 publications

(24 citation statements)

References 47 publications

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“…First, we state a result from [CET21], which is also a fact well-known to experts. Specifically, see [CET21, Lemma 3.3] for its proof.…”

Section: Extending Contactomorphisms Over Stein Tracesmentioning

confidence: 99%

Stein traces and characterizing slopes

Casals¹,

Etnyre²,

Kegel³

2021

Preprint

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We show that there exists an infinite family of pairwise non-isotopic Legendrian knots in the standard contact 3-sphere whose Stein traces are equivalent. This is the first example of such phenomenon. Different constructions are developed in the article, including a contact annulus twist, explicit Weinstein handlebody equivalences, and a discussion on dualizable patterns in the contact setting. These constructions can be used to systematically construct distinct Legendrian knots in the standard contact 3-sphere with contactomorphic (−1)-surgeries and, in many cases, equivalent Stein traces. In addition, we also discuss characterizing slopes and provide results in the opposite direction, i.e. describe cases in which the Stein trace, or the contactomorphism type of an r-surgery, uniquely determines the Legendrian isotopy type.

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“…First, we state a result from [CET21], which is also a fact well-known to experts. Specifically, see [CET21, Lemma 3.3] for its proof.…”

Section: Extending Contactomorphisms Over Stein Tracesmentioning

confidence: 99%

Stein traces and characterizing slopes

Casals¹,

Etnyre²,

Kegel³

2021

Preprint

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“…As part of their main theorem they describe infinitely many different Legendrian knots such that contact (+1)-surgery on them yield tight contact manifolds with non-vanishing contact class. That Γ strong , Γ weak , and Γ Stein have infinite indegree follows similarly from [CET17]. The other statements follow from the arguments in the proof of Proposition 1.2.…”

Section: Contact Geometric Subgraphs Of γmentioning

confidence: 55%

Contact surgery graphs

Kegel¹,

Onaran²

2022

Preprint

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“…We refer the interested reader to eg. [17,4,44,29,35,13,5,27,6,1,31]. In another direction, if one allows Lagrangian fillings to have double points, then it is shown in [41] that any augmentation to F 2 can be induced in some appropriate manner by an immersed exact Lagrangian filling.…”

Section: Introductionmentioning

confidence: 99%

Non-fillable augmentations of twist knots

Gao¹,

Rutherford²

2021

Preprint

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We establish new examples of augmentations of Legendrian twist knots that cannot be induced by orientable Lagrangian fillings. To do so, we use a version of the Seidel-Ekholm-Dimitroglou Rizell isomorphism with local coefficients to show that any Lagrangian filling point in the augmentation variety of a Legendrian knot must lie in the injective image of an algebraic torus with dimension equal to the first Betti number of the filling. This is a Floer-theoretic version of a result from microlocal sheaf theory. For the augmentations in question, we show that no such algebraic torus can exist.

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Symplectic Fillings, Contact Surgeries, and Lagrangian Disks

Cited by 18 publications

References 47 publications

Stein traces and characterizing slopes

Stein traces and characterizing slopes

Contact surgery graphs

Non-fillable augmentations of twist knots

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