Surfaces in 4-manifolds
The study of knotted surfaces in 4-manifolds is analogous to that of knotted circles in 3-manifolds. The motivations are similar: understanding cobordisms and geometric structures, but additionally motivated by the relationship between surfaces and exotic smooth structures on 4-manifolds. (Un?)fortunately, basically all “interesting” knot invariants don’t have analogues in 4D, and many classical theorems about knots are not true in 4D. I’ll talk about obstructions to isotopy and concordance of some surfaces in 4-manifolds, and maybe the relationship to smooth structures and h-cobordisms.