Parametrizing Fuchsian Subgroups of the Bianchi Groups

Abstract

Let d be a positive square-free integer and let O d denote the ring of integers in . The groups PSL 2 (O d ) are collectively known as the Bianchi groups and have been widely studied from the viewpoints of group theory, number theory and low-dimensional topology. The interest of the present article is in geometric Fuchsian subgroups of the groups PSL 2 (O d ). Clearly PSL 2 is such a subgroup; however results of [18], [19] show that the Bianchi groups are rich in Fuchsian subgroups.

Locations

• Canadian Journal of Mathematics - View - PDF