On 2-bridge knots with differing smooth and topological slice genera

TL;DR

This paper presents infinitely many 2-bridge knots where the smooth and topological slice genera differ, including the first known alternating knots with this property, highlighting differences between smooth and topological knot invariants.

Contribution

It provides the first examples of alternating knots with differing smooth and topological slice genera and constructs infinitely many such 2-bridge knots.

Findings

Existence of infinitely many 2-bridge knots with differing slice genera

First known alternating knots with this property

Identification of the smallest such knot as 12a255

Abstract

We give infinitely many examples of 2-bridge knots for which the topological and smooth slice genera differ. The smallest of these is the 12-crossing knot $12a255$. These also provide the first known examples of alternating knots for which the smooth and topological genera differ.