$\mathrm{SL}_2(\mathbb R)$-representations and left-orderable surgeries of $(-2, 3, 2n+1)$-pretzel knots
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913151544459264 |
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| author | Tran, Anh T. |
| author_facet | Tran, Anh T. |
| contents | In this paper, we provide an explicit construction of continuous paths of $\mathrm{SL}_2(\mathbb R)$-representations of the knot groups of $(-2,3,2n+1)$-pretzel knots. As an application, we show that the fundamental group of the $3$-manifold obtained from the $3$-sphere by $\frac{m}{l}$-surgery along the $(-2,3,2n+1)$-pretzel knot, where $n \ge 3$ is an integer and $n \not= 4$, is left-orderable if $\frac{m}{l}< 2 \lfloor \frac{2n+4}{3} \rfloor$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathrm{SL}_2(\mathbb R)$-representations and left-orderable surgeries of $(-2, 3, 2n+1)$-pretzel knots Tran, Anh T. Geometric Topology Primary 57K18, 57K31, Secondary 57M05 In this paper, we provide an explicit construction of continuous paths of $\mathrm{SL}_2(\mathbb R)$-representations of the knot groups of $(-2,3,2n+1)$-pretzel knots. As an application, we show that the fundamental group of the $3$-manifold obtained from the $3$-sphere by $\frac{m}{l}$-surgery along the $(-2,3,2n+1)$-pretzel knot, where $n \ge 3$ is an integer and $n \not= 4$, is left-orderable if $\frac{m}{l}< 2 \lfloor \frac{2n+4}{3} \rfloor$. |
| title | $\mathrm{SL}_2(\mathbb R)$-representations and left-orderable surgeries of $(-2, 3, 2n+1)$-pretzel knots |
| topic | Geometric Topology Primary 57K18, 57K31, Secondary 57M05 |
| url | https://arxiv.org/abs/2511.10606 |