L-space knots with tunnel number >1 by experiment
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arXiv
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| Autores principales: | , , , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866911428794908672 |
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| author | Anderson, Chris Baker, Kenneth L. Gao, Xinghua Kegel, Marc Le, Khanh Miller, Kyle Onaran, Sinem Sangston, Geoffrey Tripp, Samuel Wood, Adam Wright, Ana |
| author_facet | Anderson, Chris Baker, Kenneth L. Gao, Xinghua Kegel, Marc Le, Khanh Miller, Kyle Onaran, Sinem Sangston, Geoffrey Tripp, Samuel Wood, Adam Wright, Ana |
| contents | In Dunfield's catalog of the hyperbolic manifolds in the SnapPy census which are complements of L-space knots in $S^3$, we determine that $22$ have tunnel number $2$ while the remaining all have tunnel number $1$. Notably, these $22$ manifolds contain $9$ asymmetric L-space knot complements. Furthermore, using SnapPy and KLO we find presentations of these $22$ knots as closures of positive braids that realize the Morton-Franks-Williams bound on braid index. The smallest of these has genus $12$ and braid index $4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_00790 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | L-space knots with tunnel number >1 by experiment Anderson, Chris Baker, Kenneth L. Gao, Xinghua Kegel, Marc Le, Khanh Miller, Kyle Onaran, Sinem Sangston, Geoffrey Tripp, Samuel Wood, Adam Wright, Ana Geometric Topology 57M25 In Dunfield's catalog of the hyperbolic manifolds in the SnapPy census which are complements of L-space knots in $S^3$, we determine that $22$ have tunnel number $2$ while the remaining all have tunnel number $1$. Notably, these $22$ manifolds contain $9$ asymmetric L-space knot complements. Furthermore, using SnapPy and KLO we find presentations of these $22$ knots as closures of positive braids that realize the Morton-Franks-Williams bound on braid index. The smallest of these has genus $12$ and braid index $4$. |
| title | L-space knots with tunnel number >1 by experiment |
| topic | Geometric Topology 57M25 |
| url | https://arxiv.org/abs/1909.00790 |