Surfaces in 4-manifolds and 1-stable equivalence

The Wall's stable h-cobordism theorem states that homotopy equivalent, smooth simply-connected 4-manifolds become diffeomorphic after stabilizing, i.e. connected summing with some finite number of a S^2-bundle over S^2. And, in fact, all known examples need only one stabilization to be diffeomorphic. In this talk, we will talk about the analogous stabilization question for knotted surfaces in simply-connected 4-manifolds produced by all of the known constructions based on Fintushel-Stern knot surgery. And we will prove that any pair of these knotted surfaces that preserve the fundamental groups of their complements become all diffeomorphic after single stabilization.Non UBCUnreviewedAuthor affiliation: Seoul National UniversityFacult