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

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

2009-03-26

arxiv.org/abs/0903.4517v12

Journal of Pure and Applied Algebra 215 (2011) 1443?1472

Mathematics

K-Theory and Homology

Scientific paper

10.1016/j.jpaa.2010.09.005

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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