Topologically slice knots that are not smoothly slice in any definite 4-manifold

TL;DR

This paper constructs infinitely many topologically slice knots that cannot bound smooth disks in any definite 4-manifold, and demonstrates their linear independence in the knot concordance group.

Contribution

It introduces a new class of topologically slice knots with specific smooth bounding obstructions in definite 4-manifolds, and proves their linear independence.

Findings

Existence of infinitely many such knots.

These knots cannot bound smooth null-homologous disks in any definite 4-manifold.

The knots are linearly independent in the knot concordance group.

Abstract

We prove that there exist infinitely many topologically slice knots which cannot bound a smooth null-homologous disk in any definite 4-manifold. Furthermore, we show that we can take such knots so that they are linearly independent in the the knot concordance group.