Duke Mathematical Journal

On the cuspidal cohomology of arithmetic subgroups of $\mathrm{SL}(2n)$ and the first Betti number of arithmetic $3$-manifolds

L. Clozel

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Article information

Source
Duke Math. J. Volume 55, Number 2 (1987), 475-486.

Dates
First available: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077306031

Mathematical Reviews number (MathSciNet)
MR894591

Zentralblatt MATH identifier
0648.22007

Digital Object Identifier
doi:10.1215/S0012-7094-87-05525-6

Subjects
Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11F75: Cohomology of arithmetic groups 22E46: Semisimple Lie groups and their representations 57N10: Topology of general 3-manifolds [See also 57Mxx]

Citation

Clozel, L. On the cuspidal cohomology of arithmetic subgroups of SL ( 2 n ) and the first Betti number of arithmetic 3 -manifolds. Duke Mathematical Journal 55 (1987), no. 2, 475--486. doi:10.1215/S0012-7094-87-05525-6. http://projecteuclid.org/euclid.dmj/1077306031.


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References

  • [1] A. Arthur and L. Clozel, Base change for $GL(n)$, preprint.
  • [2] E. Artin and J. Tate, Class Field Theory, Benjamin, 1968.
  • [3] A. Borel, Commensurability classes and volumes of hyperbolic $3$-manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 8 (1981), no. 1, 1–33.
  • [4] A. Borel and H. Jacquet, Automorphic forms and automorphic representations, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 1, Proc. Symp. Pure Math. XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 189–207.
  • [5] A. Borel and N. Wallach, Continuous Cohomology, Discrete Subgroups and Representations of Reductive Groups, Annals of Mathematics Studies, vol. 94, Princeton Univ. Press, Princeton, N.J., 1980.
  • [6] A. Borel, Regularization theorems in Lie algebra cohomology. Applications, Duke Math. J. 50 (1983), no. 3, 605–623.
  • [7] P. Delorme Thèse, Univ. Paris-VI, 1978.
  • [8] M. Duflo, Représentations irreductibles des groupes semi-simples complexes, Analyse harmonique sur les groupes de Lie (Sém., Nancy-Strasbourg, 1973–75), Lecture Notes in Math., vol. 497, Springer, Berlin, 1975, pp. 26–88.
  • [9] T. J. Enright, Relative Lie algebra cohomology and unitary representations of complex Lie groups, Duke Math. J. 46 (1979), no. 3, 513–525.
  • [10] H. Jacquet and R. P. Langlands, Automorphic forms on $\rm GL(2)$, Springer-Verlag, Berlin, 1970.
  • [11] H. Jacquet and J. A. Shalika, On Euler products and the classification of automorphic representations I, Amer. J. Math. 103 (1981), no. 3, 499–558.
  • [12] J.-P. Labesse and J. Schwermer, On liftings and cusp cohomology of arithmetic groups, Invent. Math. 83 (1986), no. 2, 383–401.
  • [13] B. Speh, Unitary representations of $\rm Gl(n,\,\bf R)$ with nontrivial $(\germ g,\,K)$-cohomology, Invent. Math. 71 (1983), no. 3, 443–465.
  • [14] A. Weil, On a certain type of characters of the idèle-class group of an algebraic number-field, Proceedings of the international symposium on algebraic number theory, Tokyo & Nikko, 1955, Science Council of Japan, Tokyo, 1956, Oeuvres Scientifiques, II, p. 255–61, pp. 1–7.
  • [15] B. Dodson, Solvable and nonsolvable CM-fields, Amer. J. Math. 108 (1986), no. 1, 75–93 (1986).