Exotic Structures on Smooth Four-Manifolds

Abstract

A short survey of exotic smooth structutes on 4-manifolds is given with a special emphasis on the corresponding cork structures. Along the way we discuss some of the more recent results in this direction, obtained jointly with R. Matveyev, B.Ozbagci, C.Karakurt and K.Yasui.

Isotopy of the Dehn twist on K3 # K3 after a single stabilization

“…Ruberman [33] gave the first example of self-diffeomorphisms on 4-manifolds that are isotopic to the identity in the topological category, but not smoothly so. Further examples are given by Auckly, Kim, Melvin and Ruberman [5], Akbulut [3], Baraglia and Konno [8] and Kronheimer and Mrowka [26].…”

“…In the large families of examples (of embedded surfaces and self-diffeomorphisms) established in Akbulut [3] and Auckly, Kim, Melvin and Ruberman [5], exactly one stabilization is needed.…”