A Compactness Result for $\mathcal{H}-$holomorphic Curves in Symplectizations

Doicu, Alexandru; Fuchs, Urs

doi:10.48550/arxiv.1802.08991

Cited by 1 publication

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References 12 publications

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“…In Section 5 we study O via analysis of holomorphic curves which are perturbed in the sense of [Ab11,AbCH05]. Contrasting with Doicu and Fuchs' [DF18], our perturbation terms are unbounded, and this unboundedness is leveraged to count curves in special cases. The examples of Section 5 also demonstrate that M Λ /R ≃ O −1 (0) can not typically be understood in an entirely combinatorial fashion when Σ = D.…”

Section: Introductionmentioning

confidence: 99%

Simplified SFT moduli spaces for Legendrian links

Avdek¹

2021

Preprint

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Let Λ ⊂ (R 3 , ξ std ) be a Legendrian link in the standard contact Euclidean space. We are interested in studying holomorphic curves U in R × R 3 ≃ R × R × C with boundary on R × Λ whose domains are compact, connected Riemann surfaces with boundary punctures removed Σ ′ , allowing for positive genus or multiple boundary components. When χ(Σ ′ ) < 1, the moduli space can be seen as the zero locus of a function O whose domain is a moduli space of holomorphic maps to C and whose target is H 1 (Σ ′ ). In general, O −1 (0) is not combinatorially computable from the Lagrangian projection, π C . However, after a Legendrian isotopy, every such Λ can be made left-right-simple. With this condition in place, any holomorphic curve U(1) of index 1 is a disk with one or two positive punctures for which π C • U is an embedding.(2) of index 2 is either a disk or an annulus with π C • U simply covered and without interior critical points. Therefore, the differential of any SFT invariant defined by counting index 1 curves on (possibly multiple parallel copies of) Λ is combinatorially computable using only the disks of rational SFT.

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Section: Introductionmentioning

confidence: 99%

Simplified SFT moduli spaces for Legendrian links

Avdek¹

2021

Preprint

View full text Add to dashboard Cite

show abstract

A Compactness Result for $\mathcal{H}-$holomorphic Curves in Symplectizations

Cited by 1 publication

References 12 publications

Simplified SFT moduli spaces for Legendrian links

Simplified SFT moduli spaces for Legendrian links

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