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# Special Colloquium

Tuesday, December 10, 2019 — 3:00 PM EST

Maggie Miller, Princeton University

"Light bulbs in 4-manifolds"

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. (This setting is motivated by smooth $s$-cobordisms.) Schwartz later showed that this 2-torsion condition is necessary, and Schneiderman and Teichner then obstructed the isotopy whenever this condition fails. I weakened the hypothesis on $R$ and $R'$ by allowing $R'$ not to have a dual (motivated by topological $s$-cobordisms) and showed that the spheres are still smoothly concordant.

I will talk about these various definitions and theorems as well as current joint work with Michael Klug obstructing concordance in the case that the condition on 2-torsion in $\pi_1(X)$ fails.

MC 5501

### May 2021

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