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Algebraic overtwistedness of contact $(+1)$-surgeries via augmented Floer theories
We prove that contact $(+1)$-surgery along a Legendrian $n$-sphere $Λ\subset(\mathbb{S}^{2n+1},ξ_{\mathrm{std}})$ with \[ \mathrm{tb}(Λ)\ne (-1)^{\frac{n(n-1)}{2}+1} \] has vanishing contact homology. In dimension three, this produces new examples of tight algebraically overtwisted contact manifolds
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