# The integral homology of $PSL_2$ of imaginary quadratic integers with non-trivial class group

Abstract : We show that a cellular complex described by Floege allows to determine the integral homology of the Bianchi groups $PSL_2(O_{-m})$, where $O_{-m}$ is the ring of integers of an imaginary quadratic number field $\rationals[\sqrt{-m}]$ for a square-free natural number $m$. We use this to compute in the cases m = 5, 6, 10, 13 and 15 with non-trivial class group the integral homology of $PSL_2(O_{-m})$, which before was known only in the cases m = 1, 2, 3, 7 and 11 with trivial class group.
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Journal articles

Cited literature [23 references]

https://hal.archives-ouvertes.fr/hal-00370722
Contributor : Alexander Rahm <>
Submitted on : Monday, September 13, 2010 - 12:01:58 PM
Last modification on : Tuesday, May 11, 2021 - 11:36:03 AM
Long-term archiving on: : Tuesday, December 14, 2010 - 2:43:18 AM

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Alexander Rahm, Mathias Fuchs. The integral homology of $PSL_2$ of imaginary quadratic integers with non-trivial class group. Journal of Pure and Applied Algebra, Elsevier, 2011, 215, pp.1443-1472. ⟨10.1016/j.jpaa.2010.09.005⟩. ⟨hal-00370722v12⟩

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