SPEAKER:  Maggie Miller (Princeton)

TITLE:  Concordance of Light Bulbs

ABSTRACT: 

ABSTRACT: In 2017, Gabai proved the light bulb theorem: if R and R0 are 2- spheres in a 4-manifold X which are homotopic and have a common dual (i.e. R and R0 are \light bulbs"), then (modulo a statement about 2-torsion in 1(X)), they are smoothly isotopic. (This setting is motivated by handle cancellation of smooth cobordisms of 4-manifolds.) Schwartz later showed that this 2-torsion hypothesis is necessary, and Schneiderman and Teichner then gave an obstruction in the form of an invariant fq associated to a pair of homotopic spheres that vanishes on light bulbs if and only if they are isotopic.

I consider 2-spheres R and R0 in a 4-manifold X which are homotopic, but when only R has a dual (i.e. R and R0 are \algebraic light bulbs"). In this setting, I prove that R and R0 are smoothly concordant with the same 2-torsion hypothesis as Gabai { in general, they need not be isotopic. (This setting is motivated by handle cancellation of topological cobordisms of 4-manifolds.) I will talk about this work as well as current joint work with Michael Klug rede ning fq to prove that this invariant vanishes on algebraic light bulbs if and only if they are concordant.

Part of this talk is about joint work with Michael Klug.