Kouichi YASUI

Email kyasui(
Keywords 4-manifolds, smooth structures, handlebodies, Stein structures

I mainly study 4-manifolds. I am particularly interested in smooth structures of 4-manifolds. Regarding smooth structures on manifolds, the dimension four is still mysterious and has properties very different from other dimensions. For example, it is the unique dimension that admits an exotic (i.e. homeomorphic but non-diffeomorphic) smooth structure on the Euclidean space. On the other hand, it is a simple dimension in the sense that we can see 4-manifolds, by taking 3-dimensional (2-dimensional) informations from their handlebody (fiber) structures. I also work on applications of 4-dimensional topology to related research fields such as knot theory and contact structures.