Topologically slice $(1,1)$-knots which are not smoothly slice

TL;DR

This paper demonstrates the existence of infinitely many (1,1)-knots that are topologically slice but not smoothly slice, confirming a conjecture and highlighting differences between topological and smooth knot sliceness.

Contribution

It proves the conjecture by Béla Rácz that infinitely many (1,1)-knots are topologically slice but not smoothly slice.

Findings

Existence of infinitely many such knots confirmed.

Differentiation between topological and smooth sliceness established.

Supports the conjecture proposed by Rácz.

Abstract

We prove that there are infinitely many $(1,1)$-knots which are topologically slice, but not smoothly slice, which was a conjecture proposed by B\'ela Andr\'as R\'acz.