Conjugacy classes of autohomeomorphisms of $\mathbb{N}^*$

TL;DR

This paper discusses open problems concerning the classification of autohomeomorphisms of the Stone-Čech remainder of the natural numbers, focusing on their conjugacy classes.

Contribution

It introduces and explores specific problems related to the structure and classification of conjugacy classes in the automorphism group of sterch space .

Findings

Identifies key open problems in classifying conjugacy classes.

Highlights the complexity of automorphism groups of .

Provides a framework for future research in topological automorphisms.

Abstract

We present some problems related to the conjugacy classes of $\mathsf{Aut}(\mathbb{N}^*)$.