Reflective and quasi-reflective Bianchi groups

Abstract

A discrete subgroup of the group of isometries of the hyperbolic space is called reflective if up to a finite index it is generated by reflections in hyperplanes. The main result of this paper is a complete classification of the reflective (and quasi-reflective) subgroups among the Bianchi groups and their extensions.

arXiv comment18 pages, 4 figures; revised following referees comments; to appear in Transform. Groups