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Geometry and Topology Seminar

Friday, April 23, 2021
3:00pm to 4:00pm
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Online Event
The failure of the 4D light bulb theorem with dual spheres of non-zero square
Hannah Schwartz, Department of Mathematics, Princeton University,

Examples of surfaces embedded in a 4-manifold that are homotopic but not isotopic are neither rare nor surprising. It is then quite amazing that, in settings such as the recent 4D light bulb theorems of both Gabai and Schneiderman-Teichner, the existence of an embedded sphere of square zero intersecting a surface transversally in a single point has the power to "upgrade" a homotopy of that surface into a smooth isotopy. We will discuss the limitations of this phenonemon, using contractible 4-manifolds called corks to produce homotopic spheres in a 4-manifold with a common dual of non-zero square that are not smoothly isotopic.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit