CWR sequence of invariants of alternating links and its properties
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918032494821376 |
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| author | Jablonowski, Michal |
| author_facet | Jablonowski, Michal |
| contents | We present the $CWR$ invariant, a new invariant for alternating links, which builds upon and generalizes the $WRP$ invariant. The $CWR$ invariant is an array of two-variable polynomials that provides a stronger invariant compared to the $WRP$ invariant. We compare the strength of our invariant with the classical HOMFLYPT, Kauffman $3$-variable, and Kauffman $2$-variable polynomials on specific knot examples. Additionally, we derive general recursive "skein" relations, and also specific formulas for the initial components of the $CWR$ invariant using weighted adjacency matrices of modified Tait graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_04987 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CWR sequence of invariants of alternating links and its properties Jablonowski, Michal Geometric Topology Combinatorics We present the $CWR$ invariant, a new invariant for alternating links, which builds upon and generalizes the $WRP$ invariant. The $CWR$ invariant is an array of two-variable polynomials that provides a stronger invariant compared to the $WRP$ invariant. We compare the strength of our invariant with the classical HOMFLYPT, Kauffman $3$-variable, and Kauffman $2$-variable polynomials on specific knot examples. Additionally, we derive general recursive "skein" relations, and also specific formulas for the initial components of the $CWR$ invariant using weighted adjacency matrices of modified Tait graphs. |
| title | CWR sequence of invariants of alternating links and its properties |
| topic | Geometric Topology Combinatorics |
| url | https://arxiv.org/abs/2406.04987 |