Legendrian lens space surgeries
Hansj\"org Geiges, Sinem Onaran

TL;DR
This paper demonstrates that all tight contact structures on certain lens spaces can be constructed via a single Legendrian surgery on a specific negative torus knot in the 3-sphere, unifying their construction.
Contribution
It provides a unified method to realize all tight contact structures on specified lens spaces through Legendrian surgeries on a particular class of knots.
Findings
All tight contact structures on lens spaces $L(ns^2-s+1,s^2)$ are obtainable via Legendrian surgery.
A single Legendrian surgery suffices for these constructions.
The method applies to both tight and overtwisted contact structures on the 3-sphere.
Abstract
We show that every tight contact structure on any of the lens spaces with , , can be obtained by a single Legendrian surgery along a suitable Legendrian realisation of the negative torus knot in the tight or an overtwisted contact structure on the 3-sphere.
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