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On the Kauffman-Jones polynomial for virtual singular links

By Carmen Caprau and Kelsey Friesen

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.Comment: 20 pages; typos correcte

Topics: Mathematics - Geometric Topology, 57M27, 57M25
Year: 2019
OAI identifier: oai:arXiv.org:1610.02691

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