Classification of Hyperbolic Dehn fillings II: Quadratic case
Abstract
This paper is subsequent to [5]. In this paper, we extend the classification of hyperbolic Dehn fillings with sufficiently large coefficients by addressing the remaining case not covered in [5]. Specifically, by considering the case in which the two cusp shapes lie in the same quadratic field, we obtain the complete classification under a mild assumption satisfied by most manifolds. The content of this paper is not limited to the classification of hyperbolic Dehn fillings. Along the way, we also classify key types of automorphisms of the holonomy variety of a two-cusped hyperbolic -manifold and uncover an intriguing hidden structure in the complex volume of certain manifolds. Concrete examples illustrating these phenomena were discovered by S. Oh, and we elaborate on them in this paper. All the results presented here appear to be effective. In the third paper of this series, joint with S. Oh, we will provide examples confirming the optimality of our results.
Keywords
Cite
@article{arxiv.2503.12011,
title = {Classification of Hyperbolic Dehn fillings II: Quadratic case},
author = {BoGwang Jeon},
journal= {arXiv preprint arXiv:2503.12011},
year = {2025}
}
Comments
(i) An important case from [5] missing in the first version is now included as Theorem 1.5. (ii) The paper has been substantially rewritten. The main results have been refined, and several proofs have been simplified to improve readability. (iii) Examples illustrating several of the main results proved here were discovered by S. Oh, and we elaborate on them further in this revision