Work

Several families of incommensurable noncompact hyperbolic Coxeter polytopes

Year: 2026

Type: preprint

Abstract: We classify all 141 finite-volume hyperbolic Coxeter five-dimensional polytopes with eight facets, of which 125 are noncompact. Using maximal-cusp density and a noncompact analog of Bogachev-Douba-Raimbault's argument, we construct infinitely many pairwise incommensurable noncompact Coxeter polytopes in dimensions 4, 5, 6, 7, and 9, with the number of commensurability classes growing at least exponentially in volume.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2607.14715

Authors: Guo, Lizi, Ma, Jiming, Zang, Yourong, Zheng, Fangting

Institution: University of Wisconsin–Madison

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Natural Science Foundation of China

Award: G4000309048

OpenAlex ID: W7169587101

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