Negative contact surgery on Legendrian non-simple knots
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 ofLegendrian 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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2024
- DOI:
- 10.48550/arXiv.2405.00855
- arXiv:
- arXiv:2405.00855
- Bibcode:
- 2024arXiv240500855W
- Keywords:
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- Mathematics - Geometric Topology
- E-Print:
- 24 pages