Bianchi Orbifolds of Small Discriminant

Abstract

This brief report (6 pages) was written in 1983 but never published. It concerns the hyperbolic 3-orbifolds obtained as quotients of hyperbolic 3-space by the group of invertible 2 by 2 matrices whose entries are integers in the imaginary quadratic extension of Q of discriminant D. For values D > -100 the topological type of this orbifold is tabulated, and in the cases when the topological type is a punctured 3-sphere, the singular locus of the orbifold is drawn. A few miscellaneous comments about these orbifolds are included. The tables and pictures are based on Bob Riley's computer calculations of Ford domains and face pairings. Nothing is said about later developments after 1983. The pictures are also viewable on my webpage in a perhaps more convenient format; see http://math.cornell.edu/~hatcher