Equivalent non-isotopic spheres in 4-manifolds
Geometric Topology
2019-08-07 v3
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.
Cite
@article{arxiv.1806.07541,
title = {Equivalent non-isotopic spheres in 4-manifolds},
author = {Hannah R. Schwartz},
journal= {arXiv preprint arXiv:1806.07541},
year = {2019}
}
Comments
Final version, accepted for publication by the Journal of Topology