Negative contact surgery on Legendrian non-simple knots

Shunyu Wan; Hugo Zhou

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arXiv · 2405.00855

Negative contact surgery on Legendrian non-simple knots

Shunyu Wan·Hugo Zhou

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Abstract

We prove that for any pair of Legendrian representatives of the Chekanov-Eliashberg twist knots with different LOSS invariants, any negative rational contact $r$-surgery with $r\neq -1$ always gives rise to different contact 3-manifolds distinguished by their contact invariants. This gives the first examples of pairs of Legendrian knots with the same classical invariants but distinct contact $r$-surgeries for all negative rational number $r$. We also generalize the statement from the twist knots to a certain families of two-bridge knots.

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Shunyu Wan, Hugo Zhou. 2024-05-01. Negative contact surgery on Legendrian non-simple knots. https://arxiv.org/abs/2405.00855

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