On contact surgery

Etnyre, John

doi:10.1090/S0002-9939-08-09278-2

On contact surgery
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by John B. Etnyre

Proc. Amer. Math. Soc. 136 (2008), 3355-3362

DOI: https://doi.org/10.1090/S0002-9939-08-09278-2

Published electronically: April 30, 2008

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Abstract:

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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