Chirality of torus-covering $T^2$-links of degree three
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| Format: | Preprint |
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2026
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| _version_ | 1866914461115219968 |
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| author | Bekki, Hohto Kadokami, Teruhisa Nakamura, Inasa |
| author_facet | Bekki, Hohto Kadokami, Teruhisa Nakamura, Inasa |
| contents | A torus-covering $T^2$-link of degree $n$ is a surface-link consisting of tori, in the form of an unbranched covering of degree $n$ over the standard torus. We focus on a torus-covering $T^2$-link of degree 3, which is determined by a pair $(a,b)$ of 3-braids satisfying $ab=ba$, denoted by $\mathcal{S}_3(a,b)$. We investigate to what extent the chirality of $\mathcal{S}_3(a,b)$ is detected by invariants such as the triple linking numbers, the number of Fox $p$-colorings, and the quandle cocycle invariant associated with $p$-colorings. In particular, we determine the quandle cocycle invariant for $\mathcal{S}_3(a,b)$ associated with tri-colorings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_07724 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chirality of torus-covering $T^2$-links of degree three Bekki, Hohto Kadokami, Teruhisa Nakamura, Inasa Geometric Topology Primary: 57K45, Secondary: 57M05, 57K12 A torus-covering $T^2$-link of degree $n$ is a surface-link consisting of tori, in the form of an unbranched covering of degree $n$ over the standard torus. We focus on a torus-covering $T^2$-link of degree 3, which is determined by a pair $(a,b)$ of 3-braids satisfying $ab=ba$, denoted by $\mathcal{S}_3(a,b)$. We investigate to what extent the chirality of $\mathcal{S}_3(a,b)$ is detected by invariants such as the triple linking numbers, the number of Fox $p$-colorings, and the quandle cocycle invariant associated with $p$-colorings. In particular, we determine the quandle cocycle invariant for $\mathcal{S}_3(a,b)$ associated with tri-colorings. |
| title | Chirality of torus-covering $T^2$-links of degree three |
| topic | Geometric Topology Primary: 57K45, Secondary: 57M05, 57K12 |
| url | https://arxiv.org/abs/2604.07724 |