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On Superintegral Kleinian Sphere Packings, Bugs, and Arithmetic Groups
[article]
2021
arXiv
pre-print
We develop the notion of a Kleinian Sphere Packing, a generalization of "crystallographic" (Apollonian-like) sphere packings defined by Kontorovich-Nakamura [KN19]. Unlike crystallographic packings, Kleinian packings exist in all dimensions, as do "superintegral" such. We extend the Arithmeticity Theorem to Kleinian packings, that is, the superintegral ones come from Q-arithmetic lattices of simplest type. The same holds for more general objects we call Kleinian Bugs, in which the spheres need
arXiv:2104.13838v1
fatcat:ih57yictive5foes3gqr3onp3i