Kleinian 球填充、反射群与算术性
Kleinian sphere packings, reflection groups, and arithmeticity
AI总结：
本文研究Kleinian球填充等相关问题，解决了高维晶体球填充存在性难题，提出几何加倍构造方法并探究真整填充，技术依托洛伦兹二次型等相关计算。
摘要：
本文研究由 Kontorovich 与 Nakamura 于 2017 年首次提出、后由 Kapovich 与 Kontorovich 于 2021 年进一步探究的晶体球填充和 Kleinian 球填充。我们特别解决了 Kontorovich 和 Nakamura 提出的特定高维空间中晶体球填充的存在性问题。此外，我们提出了一种几何加倍方法，可从部分不含孤立根的 Coxeter 多面体构造球填充，并研究了“真整”填充（即整填充但非超整填充）。我们的技术大量依赖洛伦兹二次型、其正交群及相关高维双曲多面体的计算。
英文摘要：
In this paper we study crystallographic sphere packings and Kleinian sphere packings, introduced first by Kontorovich and Nakamura in 2017 and then studied further by Kapovich and Kontorovich in 2021. In particular, we solve the problem of existence of crystallographic sphere packings in certain higher dimensions posed by Kontorovich and Nakamura. In addition, we present a geometric doubling procedure allowing to obtain sphere packings from some Coxeter polyhedra without isolated roots, and study "properly integral" packings (that is, ones which are integral but not superintegral). Our techniques rely extensively on computations with Lorentzian quadratic forms, their orthogonal groups, and associated higher-dimensional hyperbolic polyhedra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
