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In this paper, we study contact surgeries along Legendrian links in the standard contact 3-sphere. On one hand, we use algebraic methods to prove the vanishing of the contact Ozsváth–Szabó invariant for contact (+1)-surgery along certain Legendrian two-component links. The main tool is a link surgery formula for Heegaard Floer homology developed by Manolescu and Ozsváth. On the other hand, we use contact-geometric argument to show the overtwistedness of the contact 3-manifolds obtained by contact (+1)-surgeries along Legendrian two-component links whose two components are linked in some special configurations.
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Fan Ding, Youlin Li, Zhongtao Wu, Contact (+1)-surgeries along Legendrian two-component links. Quantum Topol. 11 (2020), no. 2, pp. 295–321DOI 10.4171/QT/136