On a homotopy $4$-sphere

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.

The contents of this paper is transferred to the replacement submission of arXiv:1912.11804

References in corpus (3)

• Homotopy $4$-spheres associated to an infinite order loose cork
• Cork twists and automorphisms of $3$-manifolds
• On an infinite order cork automorphisms