Infinite not contact isotopic embeddings in $(S^{2n-1},\xi_{\mathrm{std}})$ for $n\ge 4$

TL;DR

This paper demonstrates the existence of infinitely many formally contact isotopic embeddings that are not contact isotopic in high-dimensional spheres, resolving a conjecture for all but the three-dimensional case.

Contribution

It proves the existence of infinitely many non-contact isotopic embeddings in high dimensions, advancing understanding in contact topology.

Findings

Infinitely many formally contact isotopic embeddings are not contact isotopic for n≥4.

Resolves a conjecture of Casals and Etnyre for n≥4.

The proof avoids using Floer theory or SFT surgery formulas.

Abstract

For $n\ge 4$, we show that there are infinitely many formally contact isotopic embeddings of $(ST^*S^{n-1},\xi_{\mathrm{std}})$ to $(S^{2n-1},\xi_{\mathrm{std}})$ that are not contact isotopic. This resolves a conjecture of Casals and Etnyre except for the $n=3$ case. The argument does not appeal to the surgery formula of critical handle attachment for Floer theory/SFT.