On the Slice-Ribbon Conjecture for Montesinos knots

TL;DR

This paper proves the slice-ribbon conjecture for a broad class of Montesinos knots using Donaldson's theorem, advancing understanding of knot slicing and ribbon properties.

Contribution

It introduces a novel application of Donaldson's theorem to confirm the conjecture for many Montesinos knots, expanding the class of knots known to satisfy it.

Findings

Confirmed the slice-ribbon conjecture for a large family of Montesinos knots.

Demonstrated the effectiveness of Donaldson's theorem in knot theory.

Provided new insights into the structure of definite 4-manifolds related to knots.

Abstract

We establish the slice-ribbon conjecture for a large family of Montesinos' knots by means of Donaldson's theorem on the intersection forms of definite 4-manifolds.