Remarks on some maximal subgroups of $F$ and on the $\vec{F}$-index of knots
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2019
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| _version_ | 1866910185645146112 |
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| author | Aiello, Valeriano |
| author_facet | Aiello, Valeriano |
| contents | We demonstrate that three maximal subgroups of infinite index in the rectangular subgroup \( K_{(2,2)} \) of the Thompson group \( F \), each containing Jones's \( 3 \)-colorable subgroup \( \mathcal{F} \), can be characterized as stabilizer subgroups. Additionally, we show that the \( \vec{F} \)-index, an elementary knot invariant introduced thanks to Jones's construction of knots from Thompson groups, may increase at most by $3$ after changing the orientation of a knot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_05045 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Remarks on some maximal subgroups of $F$ and on the $\vec{F}$-index of knots Aiello, Valeriano Geometric Topology Group Theory We demonstrate that three maximal subgroups of infinite index in the rectangular subgroup \( K_{(2,2)} \) of the Thompson group \( F \), each containing Jones's \( 3 \)-colorable subgroup \( \mathcal{F} \), can be characterized as stabilizer subgroups. Additionally, we show that the \( \vec{F} \)-index, an elementary knot invariant introduced thanks to Jones's construction of knots from Thompson groups, may increase at most by $3$ after changing the orientation of a knot. |
| title | Remarks on some maximal subgroups of $F$ and on the $\vec{F}$-index of knots |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/1910.05045 |