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Geometry-Topology Seminar

Tuesday, April 30, 2019 - 4:30pm

Hannah Schwartz

Bryn Mawr College


University of Pennsylvania

DRL 4N30

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.