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Tight contact structures via admissible transverse surgery

Department of Mathematics, University of California, Berkeley, CA, USA

https://doi.org/10.1142/S0218216519500329Cited by:1 (Source: Crossref)

Abstract

We investigate the line between tight and overtwisted for surgeries on fibered transverse knots in contact 3-manifolds. When the contact structure $ξ_{K}$ $ξ_{K}$ is supported by the fibered knot $K \subset M$ $K \subset M$ , we obtain a characterization of when negative surgeries result in a contact structure with nonvanishing Heegaard Floer contact class. To do this, we leverage information about the contact structure $ξ_{\bar{K}}$ $ξ_{\bar{K}}$ supported by the mirror knot $\bar{K} \subset - M$ $\bar{K} \subset - M$ . We derive several corollaries about the existence of tight contact structures, L-space knots outside $S^{3}$ $S^{3}$ , nonplanar contact structures, and nonplanar Legendrian knots.

Keywords:

AMSC: 57R17

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