On a homotopy $4$-sphere

TL;DR

This paper proves that a specific homotopy 4-sphere is diffeomorphic to the standard 4-sphere, clarifying its relation to loose corks and anti-corks, and provides a survey of homotopy 4-spheres.

Contribution

It offers a proof that a particular homotopy 4-sphere is standard, resolving a curiosity and connecting it to cork theory.

Findings

The homotopy 4-sphere in question is diffeomorphic to the standard S^4.

Provides a survey of known facts about homotopy 4-spheres.

Discusses the relation to infinite order loose corks and anti-corks.

Abstract

We give a brief survey of some facts about homotopy $4$-spheres \cite{a1}, then give a proof that the curious homotopy sphere constructed in \cite{a2} is in fact diffeomorphic to the standard $S^4$, and discuss its relation to infinite order loose corks and anti-corks.