Classification of (1,2)-reflective anisotropic hyperbolic lattices of rank 4

摘要

A hyperbolic lattice is said to be (1,2)-reflective if its automorphism group is generated by 1- and 2-reflections up to finite index. We prove that the fundamental polyhedron of a Q-arithmetic cocompact reflection group in three-dimensional Lobachevsky space contains an edge with sufficiently small distance between its framing faces. Using this fact, we obtain a classification of (1,2)-reflective anisotropic hyperbolic lattices of rank 4.