On contact surgery

Mathematics – Symplectic Geometry

Scientific paper

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8 pages, 2 figures

Scientific paper

In this note we show that $+1$-contact surgery on distinct Legendrian knots
frequently produces contactomorphic manifolds. We also give examples where this
happens for $-1$-contact surgery. As an amusing corollary we find overtwisted
contact structures that contain a large number of distinct Legendrian knots
with the same classical invariants and tight complements.

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