From Exotic Surfaces to Exotic Homotopy Classes of Diffeomorphisms

This represents joint work with Danny Ruberman. We will start with critical level embeddings of a pair of surfaces that are topologically isotopic but not smoothly isotopic. We will see how these surfaces may be used to construct exotic homotopy classes in the diffeomorphism group of some 4-manifolds and in spaces of embeddings. Invariants to detect exotic diffeomorphisms based on parameterized gauge theory will be defined along with a method to evaluate the invariants in some interesting cases. Given time, the talk would speculate on how these invariants could provide information about intersection patterns of surfaces in 4-manifolds tools.Non UBCUnreviewedAuthor affiliation: Kansas State UniversityFacult