The integral homology of of imaginary quadratic integers with nontrivial class group

We show that a cellular complex defined by Flöge allows us to determine the integral homology of the Bianchi groups (O−m), where O−m is the ring of integers of an imaginary quadratic number field for a square-free natural number m.In the cases of nontrivial class group, we handle the difficulties arising from the cusps associated to the nontrivial ideal classes of O−m. We use this to compute the integral homology of in the cases m=5,6,10,13 and 15, which previously was known only in the cases m=1,2,3,7 and 11 with trivial class group.