双曲Dehn填充的分类 II：二次情形
几何拓扑
2025-12-19 v3 数论
摘要
本文是[5]的后续工作。本文通过考虑尚未被[5]覆盖的剩余情形，将具有充分大系数的双曲Dehn填充的分类加以推广。具体而言，通过考虑两个尖点形状位于同一二次域的情形，我们在大多数流形所满足的温和假设下得到了完整的分类。本文的内容不限于双曲Dehn填充的分类。在此过程中，我们还对一个两尖点双曲-流形的全纯簇的关键类型自同构进行了分类，并揭示了某些流形复体积中引人入胜的隐藏结构。体现这些现象的具体例子由S. Oh发现，本文对此进行了详细阐述。本文呈现的所有结果似乎都是有效的。本系列第三篇文章将与S. Oh合作，给出确认我们结果最优性的例子。
引用
@article{arxiv.2503.12011,
title = {Classification of Hyperbolic Dehn fillings II: Quadratic case},
author = {BoGwang Jeon},
journal= {arXiv preprint arXiv:2503.12011},
year = {2025}
}
备注
(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