Pseudo knots and an obstruction to cosmetic crossings

TL;DR

This paper introduces a polynomial invariant for pseudo links, which helps identify obstructions to cosmetic crossings in classical links, advancing the understanding of link isotopies and their invariants.

Contribution

It defines a normalized bracket polynomial for pseudo links and uses it to establish an obstruction to cosmetic crossings in classical links.

Findings

Defined a normalized bracket polynomial for pseudo links

Established an obstruction to cosmetic crossings in classical links

Provided a new tool for analyzing link isotopies

Abstract

Pseudo links have two crossing types: classical crossings and indeterminate crossings. They were first introduced by Ryo Hanaki as a possible tool for analyzing images produced by electron microscopy of DNA. A normalized bracket polynomial is defined for pseudo links and then used to construct and obstruction to cosmetic crossings in classical links.