Papers › Simplified SFT moduli spaces for Legendrian links
Simplified SFT moduli spaces for Legendrian links
Russell Avdek
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We study moduli spaces ℳ of holomorphic maps U from Riemann surfaces to ℝ⁴ with boundaries on the Lagrangian cylinder over a Legendrian link Λ⊂(ℝ³, ξ_(std)). We allow our domains, Σ, to have non-trivial topology in which case ℳ is the zero locus of an obstruction function 𝒪, sending a moduli space of holomorphic maps in ℂ to H¹(Σ). In general, 𝒪⁻¹(0) is not combinatorially computable. However after a Legendrian isotopy, Λ can be made left-right-simple, implying that any U of index 1 is a disk with one or two positive punctures for which π_ℂ∘U is an embedding. Moreover, any U of index 2 is either a disk or an annulus with π_ℂ ∘U simply covered and without interior critical points. Therefore any SFT invariant of Λ is combinatorially computable using only disks with ≤2 positive punctures.
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