Torus-covering knot groups and their irreducible metabelian $SU(2)$-representations
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| Format: | Preprint |
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2019
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| _version_ | 1866912489491398656 |
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| author | Nakamura, Inasa |
| author_facet | Nakamura, Inasa |
| contents | A torus-covering $T^2$-knot is a surface-knot of genus one determined from a pair of commutative braids. For a torus-covering $T^2$-knot $F$, we determine the number of irreducible metabelian $SU(2)$-representations of the knot group of $F$ in terms of the knot determinant of $F$. It is similar to the result due to Lin for the knot group of a classical knot. Further, we investigate the number of irreducible metabelian $SU(2)$-representations using Fox's $p$-colorability. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1909_13526 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Torus-covering knot groups and their irreducible metabelian $SU(2)$-representations Nakamura, Inasa Geometric Topology A torus-covering $T^2$-knot is a surface-knot of genus one determined from a pair of commutative braids. For a torus-covering $T^2$-knot $F$, we determine the number of irreducible metabelian $SU(2)$-representations of the knot group of $F$ in terms of the knot determinant of $F$. It is similar to the result due to Lin for the knot group of a classical knot. Further, we investigate the number of irreducible metabelian $SU(2)$-representations using Fox's $p$-colorability. |
| title | Torus-covering knot groups and their irreducible metabelian $SU(2)$-representations |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/1909.13526 |