Contactomorphisms of the sphere without translated points

TL;DR

This paper constructs a specific contactomorphism of the standard sphere that lacks translated points, challenging a previously posed conjecture in contact geometry.

Contribution

It provides the first explicit example of a contactomorphism without translated points, disproving a conjecture by Sandon.

Findings

Existence of contactomorphism without translated points

Counterexample to Sandon's conjecture

Advancement in understanding contactomorphism properties

Abstract

We construct a contactomorphism of the standard sphere which does not have any translated points, providing a negative answer to a conjecture posed by Sandon.