Limiting characters at ideal points detecting twice-punctured tori
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912594930958336 |
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| author | Wang, Yi |
| author_facet | Wang, Yi |
| contents | The limiting character, introduced by Tillmann, has been studied recently in the context of Culler-Shalen theory. We extend the methods of the author's previous work to show that certain families of essential twice-punctured tori are detected by an ideal point on the character variety and determine the limiting character at these ideal points. We then provide numerous explicit examples, including certain two-bridge knots, 3-strand pretzel knots, and knots with non-integral toroidal surgeries. We also prove that the union of a once- and a twice-punctured torus inside the $(-3, 5, 5)$ or $(3, -5, -5)$ pretzel knot, both essential, is detected by an ideal point of the character variety and explicitly determine its limiting character. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limiting characters at ideal points detecting twice-punctured tori Wang, Yi Geometric Topology The limiting character, introduced by Tillmann, has been studied recently in the context of Culler-Shalen theory. We extend the methods of the author's previous work to show that certain families of essential twice-punctured tori are detected by an ideal point on the character variety and determine the limiting character at these ideal points. We then provide numerous explicit examples, including certain two-bridge knots, 3-strand pretzel knots, and knots with non-integral toroidal surgeries. We also prove that the union of a once- and a twice-punctured torus inside the $(-3, 5, 5)$ or $(3, -5, -5)$ pretzel knot, both essential, is detected by an ideal point of the character variety and explicitly determine its limiting character. |
| title | Limiting characters at ideal points detecting twice-punctured tori |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2404.06388 |