Equivalent non-isotopic spheres in 4-manifolds

Abstract

We construct infinitely many smooth oriented 4-manifolds containing pairs of homotopic, smoothly embedded 2-spheres that are not topologically isotopic, but that are equivalent by an ambient diffeomorphism inducing the identity on homology. These examples show that Gabai's recent "Generalized" 4D Lightbulb Theorem does not generalize to arbitrary 4-manifolds. In contrast, we also show that there are smoothly embedded 2-spheres that are both equivalent and topologically isotopic, but not smoothly isotopic.

arXiv commentFinal version, accepted for publication by the Journal of Topology

References in corpus (1)

• Stable isotopy in four dimensions

Cited by in corpus (5)

• Unknotting numbers of 2-spheres in the 4-sphere
• A new approach to light bulb tricks: Disks in 4-manifolds
• Concordance of Surfaces and the Freedman-Quinn Invariant
• Distances between surfaces in 4-manifolds
• Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group