Non-simplicity of isocontact embeddings in all higher dimensions

Abstract

In this article we show that in any dimension there exist infinitely many pairs of formally contact isotopic isocontact embeddings into the standard contact sphere which are not contact isotopic. This is the first example of rigidity for contact submanifolds in higher dimensions. The contact embeddings are constructed via contact push-offs of higher-dimensional Legendrian submanifolds.

24 Pages, 3 Figures. Simplification of Lemma 3.4 and inserted Minor Corrections. Final manuscript accepted in Geometric and Functional Analysis (GAFA)