Chainmail links, Dehn surgery number and $10/8$

TL;DR

This paper extends previous work on Dehn surgery obstructions by employing chainmail links and the 10/8-theorem to generate new examples of manifolds that cannot be obtained through knot surgery.

Contribution

The authors introduce a novel method using chainmail links to produce new examples of manifolds obstructed from Dehn surgery, expanding upon Liu and Piccirillo's combinatorial approach.

Findings

New examples of manifolds not obtainable via Dehn surgery on knots

Extension of the 10/8-theorem application to chainmail links

Enhanced combinatorial techniques for surgery obstructions

Abstract

Liu and Piccirillo developed a combinatorial argument that employs the 10/8-theorem to demonstrate that certain manifolds cannot be obtained via Dehn surgery on a knot. We extend their approach by creating additional examples using chainmail links.