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Infinite not contact isotopic embeddings in (S2n−1,ξstd)$(S^{2n-1},\xi _{\rm {std}})$ for n⩾4$n\geqslant 4$

Infinite not contact isotopic embeddings in (S2n−1,ξstd)$(S^{2n-1},\xi _{\rm {std}})$ for... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Infinite not contact isotopic embeddings in (S2n−1,ξstd)$(S^{2n-1},\xi _{\rm {std}})$ for n⩾4$n\geqslant 4$

Bulletin of the London Mathematical Society , Volume 55 (1) – Feb 1, 2023

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References (26)

Publisher
Wiley
Copyright
© 2023 London Mathematical Society.
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms.12717
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Feb 1, 2023

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