Knotted contractible 4-manifolds in the 4-sphere

TL;DR

This paper demonstrates that certain contractible 4-manifolds can be knotted within the 4-sphere and establishes a broad class of groups that can serve as knot groups for these embeddings.

Contribution

It introduces examples of knotted contractible 4-manifolds in the 4-sphere and proves that any finitely presented perfect group with a balanced presentation can be realized as a knot group in this context.

Findings

Existence of knotted contractible 4-manifolds in the 4-sphere

Any finitely presented perfect group with a balanced presentation can be a knot group

Broad class of groups realizable as knot groups in 4-manifolds

Abstract

Examples are given to show that some compact contractible 4-manifolds can be knotted in the 4-sphere. It is then proved that any finitely presented perfect group with a balanced presentation is a knot group for an embedding of some contractible 4-manifold in the 4-sphere.