$C^0$-flexibility of Legendrian discs in $\mathbb{R}^5$

TL;DR

This paper constructs a contact homeomorphism in five-dimensional space that transforms a Legendrian disc into a smooth disc that is nowhere Legendrian, revealing new flexibility properties in contact topology.

Contribution

It introduces a compactly supported contact homeomorphism demonstrating $C^0$-flexibility of Legendrian discs in $R^5$, a novel result in contact topology.

Findings

Existence of a contact homeomorphism mapping Legendrian to non-Legendrian discs

Demonstrates $C^0$-flexibility of Legendrian embeddings in $R^5$

Advances understanding of contact topology and Legendrian flexibility

Abstract

We construct a compactly supported contact homeomorphism of $\mathbb{R}^5$, with the standard contact structure, which maps a Legendrian disc to a smooth nowhere Legendrian disc.