Isotoping 2-spheres in 4-manifolds

TL;DR

This paper presents an example of two 2-spheres in a simply connected 4-manifold that are topologically isotopic but not smoothly isotopic, yet become smoothly isotopic after stabilization with S^2 x S^2.

Contribution

It provides a specific example illustrating the difference between topological and smooth isotopy in 4-manifolds and the effect of stabilization.

Findings

Topologically isotopic but smoothly non-isotopic 2-spheres in a 4-manifold

Stabilization by S^2 x S^2 makes them smoothly isotopic

Highlights subtle distinctions in 4-manifold topology

Abstract

Here we discuss an example of topologically isotopic but smoothly non-isotopic pair of 2-spheres in a simply connected 4-manifold, which become smoothly isotopic after stabilizing by connected summing with S^2 x S^2.