Equivalent non-isotopic spheres in 4-manifolds

Hannah R. Schwartz

doi:10.1112/topo.12121

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arXiv · 1806.07541

Equivalent non-isotopic spheres in 4-manifolds

Hannah R. Schwartz

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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.

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BibTeX RIS

Hannah R. Schwartz. 2018-06-20. Equivalent non-isotopic spheres in 4-manifolds. https://doi.org/10.1112/topo.12121

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