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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.06388 |
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Table of 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.