Michael Klug, University of California Berkeley
"Concordance of homotopic spheres in 4-manifolds"
I will discuss joint work with Maggie Miller on concordance of surfaces in 4-manifolds. In particular, I will discuss a condition that guarantees that two homotopic spheres in a 4-manifold are concordant. An invariant of a pair of homotopic spheres, called the Freedman-Quinn invariant that has been of interest in recent work of Gabai, Teichner-Schneiderman, will be discussed and we will see that it is the sole obstruction to there existing a concordance. The simply-connected case was proved by Nathan Sunukjian building on the proof by Kervaire that all 2-knots are slice and we will build on this and use many similar ideas.