# Examples of non-trivial contact mapping classes for overtwisted contact manifolds in all dimensions

## TL;DR

This paper constructs numerous examples of contactomorphisms in all dimensions that are smoothly isotopic but not contact-isotopic to the identity on overtwisted contact manifolds, highlighting complex contact topology.

## Contribution

It provides the first infinite families of such contactomorphisms in all dimensions, expanding understanding of contact mapping class groups in overtwisted manifolds.

## Key findings

- Existence of infinitely many non-trivial contact mapping classes in all dimensions.
- Construction of explicit examples of contactomorphisms not contact-isotopic to the identity.
- Demonstration that smooth isotopy does not imply contact isotopy in overtwisted manifolds.

## Abstract

We construct (infinitely many) examples in all dimensions of contactomorphisms of closed overtwisted contact manifolds that are smoothly isotopic but not contact-isotopic to the identity.