Contact (+1)-surgeries along Legendrian Two-component Links

Fan Ding; Youlin Li; Zhongtao Wu

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arXiv · 1801.02180

Contact (+1)-surgeries along Legendrian Two-component Links

Fan Ding·Youlin Li·Zhongtao Wu

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Abstract

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 Ozsv\'{a}th-Szab\'{o} 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 Ozsv\'{a}th. 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. 2018-01-07. Contact (+1)-surgeries along Legendrian Two-component Links. https://arxiv.org/abs/1801.02180

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