The integral homology of PSL(2) of imaginary quadratic integers with nontrivial class group
Rahm, Alexander D.
Rahm, Alexander D.
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http://dx.doi.org/10.1016/j.jpaa.2010.09.005
http://hdl.handle.net/10379/3789
https://doi.org/10.13025/15146
http://hdl.handle.net/10379/3789
https://doi.org/10.13025/15146
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Publication Date
2011
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Article
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Rahm, Alexander D. and Fuchs, Mathias (2011) 'The integral homology of PSL(2) of imaginary quadratic integers with nontrivial class group'. J. Pure Appl. Algebra, 215 (6):1443-1472.
Abstract
We show that a cellular complex defined by Flöge allows us 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 Q [square root -m] 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 PSL(2)(O[-m]) 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.
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Publisher DOI
10.1016/j.jpaa.2010.09.005
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Attribution-NonCommercial-NoDerivs 3.0 Ireland