The integral homology of $PSL_2$ of imaginary quadratic integers of class number two

Alexander Rahm (1, 2) , Mathias Fuchs (3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 Mathematisches Institut der Universitaet Goettingen
3 Georg-August-University = Georg-August-Universität Göttingen

We calculate the integral homology of the non-Euclidean Bianchi groups $PSL_2$ of the ring of integers of the number field $Q[\sqrt{-m}]$ for $m=5,6,10,13$, making essential use of an equivariant cellular decomposition of a retract of hyperbolic three-space due to Floege.

Mots clés: Cohomology of arithmetic groups; Discrete subgroups of Lie groups; Discontinuous groups of transformations

Domaines: K-théorie et homologie [math.KT]

Alexander Rahm, Mathias Fuchs. The integral homology of $PSL_2$ of imaginary quadratic integers of class number two. 2009. ⟨hal-00370722v3⟩