Theme

Low-dimensional Topology

My research interests are in 4-dimensional topology, and especially smooth structures of 4-manifolds. Regarding smooth structures, the dimension four has many properties very different from all other dimensions, and has been known as the most mysterious dimension. For example, the dimension four is the unique dimension that admits an exotic (i.e. homeomorphic but non-diffeomorphic) smooth structure on the Euclidean space, and many 4-manifolds admit infinitely many exotic smooth structures. On the other hand, it is a simple dimension in the sense that we can see 4-manifolds, by extracting 3-dimensional (2-dimensional) information from their handlebody (fiber) structures. Using handlebody theory, symplectic topology, and Gauge theory, I am studying smooth 4-manifolds from various points of view. I also work on applications of 4-dimensional topology to related research fields such as knot theory and contact 3-manifolds.

Contact

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