Getting a handle on the Conway knot

TL;DR

Lisa Piccirillo proved that the Conway knot is not slice, resolving a 50-year-old mathematical mystery about this specific 11-crossing knot's property in four-dimensional topology.

Contribution

The paper presents the first proof that the Conway knot is not slice, solving a long-standing open problem in knot theory.

Findings

Conway knot is not slice.

Resolved a 50-year-old open problem.

Introduced a novel proof technique.

Abstract

A knot is said to be slice if it bounds a smooth disk in the 4-ball. For 50 years, it was unknown whether a certain 11 crossing knot, called the Conway knot, was slice or not, and until recently, this was the only one of the thousands of knots with fewer than 13 crossings whose slice-status remained a mystery. We will describe Lisa Piccirillo's proof that the Conway knot is not slice. The main idea of her proof is given in the title of this article.