On Slavik Jablan's work on 4-moves

TL;DR

This paper proves that all 2-component alternating links with up to 12 crossings can be simplified to trivial or Hopf links using 4-moves, addressing a question posed by Slavik Jablan.

Contribution

It demonstrates a universal reduction method for a specific class of links, confirming Jablan's conjecture for these cases.

Findings

All 2-component alternating links with ≤12 crossings reduce to trivial or Hopf links via 4-moves.

Provides a positive answer to Jablan's question for this class of links.

Establishes a new link simplification technique for a specific link class.

Abstract

We show that every alternating link of 2-components and 12 crossings can be reduced by 4-moves to the trivial link or the Hopf link. It answers the question asked in one of the last papers by Slavik Jablan.