Classification of $(1{,}2)$-reflective anisotropic hyperbolic lattices of rank $4$
Algebraic Geometry
2019-03-27 v1 Group Theory
Geometric Topology
Number Theory
Abstract
A hyperbolic lattice is called \textit{-reflective} if its automorphism group is generated by - and -reflections up to finite index. In this paper we prove that the fundamental polyhedron of a -arithmetic cocompact reflection group in the three-dimensional Lobachevsky space contains an edge such that the distance between its framing faces is small enough. Using this fact we obtain a classification of -reflective anisotropic hyperbolic lattices of rank .
Keywords
Cite
@article{arxiv.1903.08147,
title = {Classification of $(1{,}2)$-reflective anisotropic hyperbolic lattices of rank $4$},
author = {Nikolay V. Bogachev},
journal= {arXiv preprint arXiv:1903.08147},
year = {2019}
}
Comments
17 pages, 5 figures, 1 table. arXiv admin note: text overlap with arXiv:1610.06148