Sungkyung Kang

We say that a knot is slice if it bounds a smooth disk in 4-ball and ribbon if it bounds a ribbon disk in 3-sphere. Ribbon knots are always slice, while it is unknown whether the converse, also known as the slice-ribbon conjecture, is true. The...

We say that two smooth 4-manifolds are exotic if they are homemorphic but not diffeomorphic. Wall's theorem, proven in 1964, says that when the given 4-manifolds are simply-connected, they are always diffeomorphic after sufficiently many...