Branched covering surface-knots with degree three have the simplifying numbers less than three

TL;DR

This paper proves that branched covering surface-knots of degree three have a simplifying number less than three, providing a key invariant bound in knot theory.

Contribution

It establishes a new upper bound for the simplifying number of degree three branched covering surface-knots, advancing understanding of their structure.

Findings

Branched covering surface-knots with degree three have simplifying numbers less than three.

The result constrains the complexity of such surface-knots.

Provides a new invariant bound in the study of surface-knots.

Abstract

A branched covering surface-knot is a surface-knot in the form of a branched covering over a surface-knot. For a branched covering surface-knot, we have a numerical invariant called the simplifying number. We show that branched covering surface-knots with degree three have the simplifying numbers less than three.