On slice alternating 3-braid closures

TL;DR

This paper constructs ribbon surfaces for certain alternating 3-braid closures and classifies smoothly slice knots among them using twisted Alexander polynomial obstructions.

Contribution

It introduces new ribbon surface constructions and applies twisted Alexander polynomial obstructions to classify slice knots among alternating 3-braid closures.

Findings

Ribbon surfaces of Euler characteristic one constructed for infinite families.

Classification of smoothly slice alternating 3-braid knots up to 20 crossings.

Application of twisted Alexander polynomial as an obstruction method.

Abstract

We construct ribbon surfaces of Euler characteristic one for several infinite families of alternating 3-braid closures. We also use a twisted Alexander polynomial obstruction to conclude the classification of smoothly slice knots which are closures of alternating 3-braids with up to 20 crossings.