Detection of twice-punctured tori in hyperbolic knot complements

Yi Wang

Published 2024-04-09Version 1

We extend the methods of the author's previous paper to show that certain families of essential twice-punctured tori are detected by an ideal point on the character variety, and that the limiting character at these ideal points is irreducible. This completes the proof that all punctured tori in two-bridge knots are detected by an ideal point in the $SL_2(\mathbb{C})$ character variety and initiates the study of punctured tori in pretzel knots.