Title: The integral homology of $PSL_2$ of imaginary quadratic integers with nontrivial class group

Authors: Alexander D. Rahm and Mathias Fuchs

Abstract: We show that a cellular complex defined by Floege allows to determine the integral homology of the Bianchi groups PSL_2(A), where A is the ring of integers of an imaginary quadratic number field Q(squareroot{-m}) for a square-free natural number m.
In the cases of non-trivial class group, we handle the difficulties arising from the cusps associated to the non-trivial ideal classes of A. We use this to compute in the cases m = 5, 6, 10, 13 and 15 the integral homology of PSL_2(A), which before was known only in the cases m = 1, 2, 3, 7 and 11 with trivial class group.


Alexander D. Rahm
Institut Fourier, UJF Grenoble and Math. Institut, Universitaet Goettingen
URL: http://www-fourier.ujf-grenoble.fr/~rahm/

Mathias Fuchs
Department of Bioinformatics, Center of Informatics, Statistics and Epidemiology
UMG, University of Goettingen
URL: http://www.bioinf.med.uni-goettingen.de/people/mathias_fuchs/