Alexander polynomials of simple-ribbon knots
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2019
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| _version_ | 1866910282556637184 |
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| author | Kishimoto, Kengo Shibuya, Tetsuo Tsukamoto, Tatsuya Ishikawa, Tsuneo |
| author_facet | Kishimoto, Kengo Shibuya, Tetsuo Tsukamoto, Tatsuya Ishikawa, Tsuneo |
| contents | In a previous paper, we introduced special types of fusions, so called simple-ribbon fusions on links. A knot obtained from the trivial knot by a finite sequence of simple-ribbon fusions is called a simple-ribbon knot. Every ribbon knot with <10 crossings is a simple-ribbon knot. In this paper, we give a formula for the Alexander polynomials of simple-ribbon knots. Using the formula, we determine if a knot with 10 crossings is a simple-ribbon knot. Every simple-ribbon fusion can be realized by ``elementary" simple-ribbon fusions. We call a knot a p-simple-ribbon knot if the knot is obtained from the trivial knot by a finite sequence of elementary p-simple-ribbon fusions for a fixed positive integer p. We provide a condition for a simple-ribbon knot to be both of an m-simple-ribbon knot and an n-simple-ribbon knot for positive integers m and n. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_04915 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Alexander polynomials of simple-ribbon knots Kishimoto, Kengo Shibuya, Tetsuo Tsukamoto, Tatsuya Ishikawa, Tsuneo Geometric Topology In a previous paper, we introduced special types of fusions, so called simple-ribbon fusions on links. A knot obtained from the trivial knot by a finite sequence of simple-ribbon fusions is called a simple-ribbon knot. Every ribbon knot with <10 crossings is a simple-ribbon knot. In this paper, we give a formula for the Alexander polynomials of simple-ribbon knots. Using the formula, we determine if a knot with 10 crossings is a simple-ribbon knot. Every simple-ribbon fusion can be realized by ``elementary" simple-ribbon fusions. We call a knot a p-simple-ribbon knot if the knot is obtained from the trivial knot by a finite sequence of elementary p-simple-ribbon fusions for a fixed positive integer p. We provide a condition for a simple-ribbon knot to be both of an m-simple-ribbon knot and an n-simple-ribbon knot for positive integers m and n. |
| title | Alexander polynomials of simple-ribbon knots |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/1905.04915 |