Crossing changes, Delta moves, and sharp moves on welded knots

TL;DR

This paper proves that crossing changes, Delta moves, and sharp moves can all be used as unknotting operations on welded knots, expanding the understanding of their manipulation.

Contribution

It establishes that these three moves are sufficient as unknotting operations specifically for welded knots, a significant result in knot theory.

Findings

Crossing changes are unknotting operations on welded knots.

Delta moves are unknotting operations on welded knots.

Sharp moves are unknotting operations on welded knots.

Abstract

We prove that the crossing changes, Delta moves, and sharp moves are unknotting operations on welded knots.