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Smoothly exotic spheres in four manifolds

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Hannah Schwartz
Bryn Mawr/MPIM Bonn
Tue, 2019-09-17 11:30 - 12:20
MPIM Lecture Hall

Throughout this talk, we will compare the notions of topological isotopy, smooth isotopy, and smooth equivalence (via an ambient diffeomorphism preserving homology) between homotopic $2$-spheres smoothly embedded in a $4$-manifold. In particular, we will construct pairs of spheres that are smoothly equivalent but not even topologically isotopic. Indeed, our examples show that Gabai's recent "4D Lightbulb Theorem" does not hold without the 2-torsion hypothesis.

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