The average genus of a 2-bridge knot is asymptotically linear
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916901628674048 |
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| author | Cohen, Moshe Lowrance, Adam M. |
| author_facet | Cohen, Moshe Lowrance, Adam M. |
| contents | Experimental work suggests that the Seifert genus of a knot grows linearly with respect to the crossing number of the knot. In this article, we use a billiard table model for $2$-bridge or rational knots to show that the average genus of a $2$-bridge knot with crossing number $c$ asymptotically approaches $c/4+1/12$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_06122 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The average genus of a 2-bridge knot is asymptotically linear Cohen, Moshe Lowrance, Adam M. Geometric Topology 57K10 Experimental work suggests that the Seifert genus of a knot grows linearly with respect to the crossing number of the knot. In this article, we use a billiard table model for $2$-bridge or rational knots to show that the average genus of a $2$-bridge knot with crossing number $c$ asymptotically approaches $c/4+1/12$. |
| title | The average genus of a 2-bridge knot is asymptotically linear |
| topic | Geometric Topology 57K10 |
| url | https://arxiv.org/abs/2205.06122 |