Quasi-arithmetic hyperbolic Coxeter prisms
Geometric Topology
2024-04-26 v3 Group Theory
Number Theory
Abstract
In 1974, Kaplinskaja classified all simplicial straight hyperbolic Coxeter prisms. In this paper, we determine precisely which of these prisms are properly quasi-arithmetic or arithmetic. We also present some observations regarding commensurability classes and systoles of the associated orbifolds.
Cite
@article{arxiv.2312.17193,
title = {Quasi-arithmetic hyperbolic Coxeter prisms},
author = {Nikolay Bogachev and Khusrav Yorov},
journal= {arXiv preprint arXiv:2312.17193},
year = {2024}
}
Comments
13 pages, 7 tables. Due to a technical mistake, the proof of Theorem 1.5 from the previous version is wrong, and this Theorem 1.5 is now removed from the paper. It doesn't affect the main results of the paper. Thus, the question of existence of uniform quasi-arithmetic hyperbolic lattices with an isotropic invariant form remains open even in dimension 3. arXiv admin note: text overlap with arXiv:2304.12590