Smoothly slice knots with Alexander polynomial 1 and high unknotting number

TL;DR

This paper demonstrates the existence of a special class of knots that are smoothly doubly slice, amphicheiral, have Alexander polynomial 1, and an unknotting number of 5, expanding understanding of knot properties.

Contribution

It establishes the existence of a specific type of knot with combined properties previously not known to coexist.

Findings

Existence of a smoothly doubly slice, amphicheiral knot with Alexander polynomial 1 and unknotting number 5.

Provides new examples of knots with complex property combinations.

Advances the classification of knots based on their smooth and algebraic properties.

Abstract

We prove the existence of a smoothly doubly slice, amphicheiral knot with Alexander polynomial 1 and unknotting number 5.