Infinitely many smoothly slice knots admit topological slice discs that are non-approximable by smooth slice discs, even up to isotopy.
Freedman and Frank Quinn, Topology of 4 -manifolds, Princeton Mathematical Series, vol
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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.