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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Cohomology of certain congruence subgroups of the modular group

Author(s): Frank Williams; Robert J. Wisner
Journal: Proc. Amer. Math. Soc. 126 (1998), 1331-1336.
MSC (1991): Primary 20J05; Secondary 11F06
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Abstract | References | Similar articles | Additional information

Abstract: In this note we compute the integral cohomology groups of the subgroups $\Gamma _0(n)$ of $SL(2, \mathbf{Z})$ and the corresponding subgroups $P\Gamma _0(n)$ of its quotient, the classical modular group, $PSL(2, \mathbf{Z}).$


References:

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A. Adem and N. Naffah, On the cohomology of $SL_2(\mathbf{Z}[1/p]),$ to appear in the Proceedings of the Durham Symposium (1994) on Geometry and Cohomology in Group Theory.
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Y. Chuman, Generators and relations of $\Gamma _0(n),$ J. Math Kyoto Univ. 13 (1973) 381-390. MR 50:499
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S. Hesselmann, Zur Torsion der S-arithmetischer Gruppen, Bonner Mathematische Schriften, 257 (1993), 1-93. MR 95m:11053
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K. Moss, Homology of $SL(n, \mathbf{Z}[1/p]),$ Duke Mathematical Journal, 47 (1980), 803-818. MR 82b:20061
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N. Naffah, On the integral Farrell cohomology ring of $PSL_2(\mathbf Z[1/n])$, Thesis, ETH-Zurich, 1996.
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J.-P. Serre, Cohomologie des groupes discrets, Prospects in Mathematics, Annals of Math. Studies 70 (1971), 77-169. MR 52:5876
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Additional Information:

Frank Williams
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
Email: frank@nmsu.edu

Robert J. Wisner
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003

DOI: 10.1090/S0002-9939-98-04367-6
PII: S 0002-9939(98)04367-6
Received by editor(s): October 30, 1996
Additional Notes: The authors would like to thank Alejandro Adem, Ross Staffeldt, Susan Hermiller, Ray Mines, and Morris Newman for their helpful comments.
Communicated by: Ronald M. Solomon
Copyright of article: Copyright 1998, American Mathematical Society


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