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.