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

Abstract

For n ≥ 4, we show that there are infinitely many formally contact isotopic embeddings of the standard ST * S n−1 to (S 2n−1 , ξ std ) that are not contact isotopic. This answers a conjecture of Casals and Etnyre [5] except for the n = 3 case. The argument does not appeal to the surgery formulae of critical handle attachement for Floer theory/SFT.