# Tight Contact Structures via Admissible Transverse Surgery

@article{Conway2015TightCS,
title={Tight Contact Structures via Admissible Transverse Surgery},
author={James R. W. Conway},
journal={arXiv: Geometric Topology},
year={2015},
pages={1950032}
}
• James R. W. Conway
• Published 2015
• Mathematics
• arXiv: Geometric Topology
• We investigate the line between tight and overtwisted for surgeries on fibred transverse knots in contact 3-manifolds. When the contact structure $\xi_K$ is supported by the fibred knot $K \subset M$, we obtain a characterisation of when negative surgeries result in a contact structure with non-vanishing Heegaard Floer contact class. To do this, we leverage information about the contact structure $\xi_{\overline{K}}$ supported by the mirror knot $\overline{K} \subset -M$. We derive several… CONTINUE READING

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