Year: 2026
Type: preprint
Abstract: The Koebe-Andreev-Thurston theorem assigns a 3-dimensional hyperbolic reflection group to each combinatorial polyhedron. A natural question is: which of them are arithmetic? In 2016, Kontorovich-Nakamura conjectured that all arithmetic reflection groups obtained in this way are commensurable to those obtained from the tetrahedron, square pyramid, or cuboctahedron. In this paper, we prove the conjecture. It is a consequence of the following result of independent interest: all arithmetic ideal, right-angled hyperbolic polyhedra are obtained by gluing together copies of one of three ``seed'' polyhedra.
Source: arXiv (Cornell University)
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211894545
Cites:
Cited by:
Related to: