Contact (+1)-surgeries along Legendrian Two-component Links
Fan Ding, Youlin Li, Zhongtao Wu

TL;DR
This paper investigates contact (+1)-surgeries on Legendrian two-component links in the standard contact 3-sphere, demonstrating vanishing invariants and overtwistedness using algebraic and contact-geometric methods.
Contribution
It introduces new algebraic and geometric techniques to analyze contact (+1)-surgeries on Legendrian links, including a link surgery formula for Heegaard Floer homology.
Findings
Vanishing of contact Ozsváth-Szabó invariant for certain surgeries
Overtwistedness of resulting contact 3-manifolds in specific configurations
Application of link surgery formula to contact topology
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 -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 -surgeries along Legendrian two-component links whose two components are linked in some special configurations.
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Taxonomy
TopicsGeometric and Algebraic Topology · Botulinum Toxin and Related Neurological Disorders · Homotopy and Cohomology in Algebraic Topology
