Smoothly slice knots with smoothly non-approximable topological slice discs

TL;DR

This paper constructs infinitely many smoothly slice knots with topological slice discs that cannot be approximated by smooth slice discs, highlighting a fundamental distinction between smooth and topological sliceness.

Contribution

It introduces a new class of knots demonstrating the non-approximability of topological slice discs by smooth ones, advancing understanding of smooth vs. topological knot slicing.

Findings

Existence of infinitely many such knots.

Topological slice discs are not smooth-approximable.

Highlights differences between smooth and topological sliceness.

Abstract

We construct infinitely many smoothly slice knots having topological slice discs that are non-approximable by smooth slice discs.