On the Kauffman-Jones polynomial for virtual singular links

TL;DR

This paper extends the Kauffman-Jones polynomial to virtual singular links, decomposing it into two invariants that capture more detailed topological information about these links.

Contribution

The paper introduces an extension of the Kauffman-Jones polynomial to virtual singular links and demonstrates its decomposition into two invariant components.

Findings

The extended polynomial is valued in Z[A^2, A^{-2}, h].

Decomposition yields two invariants, one in Z[A^2, A^{-2}] and another in Z[A^2, A^{-2}]h.

Both components are invariants for virtual singular links.

Abstract

We extend the Kamada-Miyazawa polynomial to virtual singular links, which is valued in $\mathbb{Z}[A^2, A^{-2}, h]$. The decomposition of the resulting polynomial into two components, one in $\mathbb{Z}[A^2, A^{-2}]$ and the other in $\mathbb{Z}[A^2, A^{-2}]h$ yields the decomposition of the Kauffman-Jones polynomial of virtual singular links into two components, one in $\mathbb{Z}[A^2, A^{-2}]$ and the other in $\mathbb{Z}[A^2, A^{-2}]A^2$, where both components are invariants for virtual singular links.