On the minimal number of translated points in contact lens spaces

TL;DR

This paper proves that any contactomorphism of a standard contact lens space isotopic to the identity has at least 2n translated points, refining previous bounds and confirming a conjecture.

Contribution

It establishes a sharp lower bound of 2n translated points for contactomorphisms on contact lens spaces, improving prior results and resolving a conjecture.

Findings

Every contactomorphism isotopic to identity has at least 2n translated points.

The bound of 2n is sharp and optimal.

The result confirms a conjecture of Sandon.

Abstract

In this article, we prove that every contactomorphism of any standard contact lens space of dimension $2n-1$ that is contact-isotopic to identity has at least $2n$ translated points. This sharp lower bound refines a result of Granja-Karshon-Pabiniak-Sandon and answers a conjecture of Sandon positively.