Stable splittings of the Bianchi groups

The Bianchi groups are a collection of matrix groups that can be thought of as generalizations of PSL₂(ℤ), which can be built out of finite groups using algebraic constructions like the amalgamated product and the HNN extension. When a Bianchi group Γ’s classifying space is suspended, the space often splits into a wedge of pieces that reflect Γ’s finite subgroups. In this talk, we will review previous work in this vein and produce stable splittings for various members of the Bianchi group family.