Infinitely many smoothly slice knots admit topological slice discs that are non-approximable by smooth slice discs, even up to isotopy.
Freedman, The disk theorem for four-dimensional manifolds, Proceedings of the I nternational C ongress of M athematicians, V ol.\ 1, 2 ( W arsaw, 1983) (Warsaw), PWN, 1984, pp
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Smoothly slice knots with smoothly non-approximable topological slice discs
Infinitely many smoothly slice knots admit topological slice discs that are non-approximable by smooth slice discs, even up to isotopy.