Khovanov homology and star-like isotopies

TL;DR

This paper introduces a new link polynomial invariant based on the Jones polynomial that remains invariant under a specific class of isotopies called star-like isotopies, and provides a categorification of this polynomial.

Contribution

It defines a novel link polynomial invariant specific to star-like isotopies and offers its categorification, expanding the understanding of link invariants under restricted isotopies.

Findings

The polynomial is invariant under star-like isotopies.

Categorification of the polynomial is achieved.

The work extends link invariants to a new class of isotopies.

Abstract

A star-like isotopy for oriented links in 3-space is an isotopy which uses only Reidemeister II moves with opposite orientations and Reidemeister III moves with alternating orientations when checking the strands clockwise (or anticlockwise). We define a link polynomial derived from the Jones polynomial which is, in general, only invariant under star-like isotopies and we categorify it.