Low-dimensional topology

My research interests are in low-dimensional topology, especially in 4-dimensional topology. Regarding smooth structures on manifolds, dimension four is the most mysterious dimension and has many interesting phenomena that cannot occur in any other dimension. For example, dimension four is the unique dimension that admits an exotic (i.e., homeomorphic but non-diffeomorphic) smooth structure on the Euclidean space. On the other hand, 4-manifolds are simple objects in the sense that they admit diagrammatic presentations via handle decompositions or fiber structures, and there are numerous intriguing examples of 4-manifolds. In order to understand the world of 4-manifolds, I study constructions, restrictions, and invariants of 4-manifolds from various viewpoints. I also work on applications of 4-dimensional topology to 3-dimensional topology by using connections of 4-manifolds with knots and 3-manifolds.