Limiting characters at ideal points detecting twice-punctured tori
arXiv:2404.06388
Abstract
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 or pretzel knot, both essential, is detected by an ideal point of the character variety and explicitly determine its limiting character.
Major revision of article previously titled "Detection of twice-punctured tori in hyperbolic knot complements". 22 pages; 2 figures