论文标题
kleinian球体包装，反射组和算术
Kleinian sphere packings, reflection groups, and arithmeticity
论文作者
论文摘要
在本文中，我们研究了Kontorovich和Nakamura首先在2017年推出的晶体球形包装和Kleinian Sphere包装，然后在2021年由Kapovich和Kontorovich进一步学习。特别是，我们解决了Kontorovich和Nakamamerura在某些更高尺寸中存在的晶体球形包装存在的问题。此外，我们提出了一个几何加倍程序，可以从某些没有孤立的根部的Coxeter Polyhedra获得球形包装，并研究“正确的整合”包装（即，它是整合但不是稳固的）。我们的技术广泛依赖于洛伦兹二次形式，其正交组以及相关的高维双曲线多面体的计算。
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.
