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ˆ L k is a closed manifold L k minus a disk. The Legendrian boundary of ∂ ˆ L k is formally Legendrian isotopic to the standard unknot in ( S 2 n − 1 , ξ std )
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For n⩾4$n\geqslant 4$, we show that there are infinitely many formally contact isotopic embeddings of (ST∗Sn−1,ξstd)$(ST^*S^{n-1},\xi _{\rm {std}})$ to (S2n−1,ξstd)$(S^{2n-1},\xi _{\rm {std}})$ that are not contact isotopic. This resolves a conjecture of Casals and Etnyre (Geom. Funct. Anal. 30 (2020), no. 1, 1–33) except for the n=3$n=3$ case. The argument does not appeal to the surgery formula of critical handle attachment for Floer theory/SFT.
Bulletin of the London Mathematical Society – Wiley
Published: Feb 1, 2023
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