University of Cambridge > Talks.cam > Differential Geometry and Topology Seminar > Obstructing isotopies between surfaces in four-manifolds

Obstructing isotopies between surfaces in four-manifolds

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  • UserHannah Schwartz, MPI Bonn
  • ClockWednesday 27 November 2019, 16:00-17:00
  • HouseMR13.

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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.

This talk is part of the Differential Geometry and Topology Seminar series.

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