# Seminars & Colloquia Calendar

Topology/Geometry Seminar

## Light bulbs in 4-manifolds

#### Maggie Miller (Princeton)

Location:  Room 705
Date & time: Tuesday, 04 February 2020 at 3:50PM - 4:40PM

In 2017, Gabai proved the light bulb theorem, showing that if $$R$$ and $$R'$$ are 2-spheres homotopically embedded in a 4-manifold with a common dual, then with some condition on 2-torsion in $$\pi_1(X)$$ one can conclude that $$R$$ and $$R'$$ are smoothly isotopic. Schwartz later showed that this 2-torsion condition is necessary, and Schneiderman and Teichner then obstructed the isotopy whenever this condition fails. I showed that when $$R'$$ does not have a dual, we may still conclude the spheres are smoothly concordant.

I will talk about these various definitions and theorems as well as new joint work with Michael Klug generalizing the result on concordance to the situation where $$R$$ has an immersed dual (and $$R'$$ may have none), which is a common condition in 4-dimensional topology.

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