Obstructing isotopies between surfaces in four manifolds

Hannah Schwarz (MPI Bonn)

Monday 25th November, 2019 16:00-17:00 Maths 311B


We will first construct pairs of homotopic 2-spheres smoothly embedded in a 4-manifold that are smoothly equivalent (via an ambient diffeomorphism preserving homology) but not even topologically isotopic. Indeed, these examples show that Gabai's recent "4D Lightbulb Theorem" does not hold without the 2-torsion hypothesis. We will proceed to discuss two distinct ways of obstructing such an isotopy, as well as related invariants which can be used to obstruct an isotopy between pairs of properly embedded disks (rather than spheres) in a 4-manifold.

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