Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-01T02:46:19.211Z Has data issue: false hasContentIssue false
  • English
  • Français

On the cohomology of Fuchsian groups

Published online by Cambridge University Press:  18 May 2009

S. J. Patterson
S. J. Patterson
Affiliation:
Department of pure Mathematics and Mathematical Statistics, 16 Mill Lane, Cambridge, CB2 1SB
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The object of this paper is to redevelop the classical theory of multipliers of Fuchsian groups [16] and to attempt a classification. The language which appears most appropriate is that of group extensions and the cohomology of groups. This viewpoint is not entirely novel [12] but the entire theory has never been based on it before.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 2 , September 1975 , pp. 123 - 140
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

REFERENCES

1.Bers, L., Spaces of Riemann surfaces, Proc. Int. Cong. Math. Edinburgh (Cambridge, 1960).Google Scholar
2.Chern, S. S., Complex manifolds without potential theory (Van Nostrand, 1967).Google Scholar
3.Dyer, J. and Lewittes, J., Möbius transformations and matrices (Preprint).Google Scholar
4.Elstrodt, J., Die Resotvente zum Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene, I, II, III, Math. Ann. 203 (1973), 295–330, Math. Zeit. 132 (1973), 99–134, Math. Ann. 208 (1974), 99–132.CrossRefGoogle Scholar
5.Fadeev, L. D., Expansion in eigenfunctions of the Laplace operator on the fundamental domain of a discrete group on the Lobačevskiĭ plane. Trans. Moscow Math. Soc. 17 (1967), 357–386.Google Scholar
6.Gel'fand, I. M., Graev, M. I. and Pyatetskii-Shapiro, I. I., Representation theory and automorphic functions (Saunders, 1969).Google Scholar
7.Godement, R., Cohomology des groupes discontinues (Sém. Bourbaki (1954) No. 90).Google Scholar
8.Goldstein, L. J., Dedekind sums for a Fuchsian group, I., Nagoya Math. J. 50 (1973), 21–47.CrossRefGoogle Scholar
9.Kra, I., Automorphic forms and Kleinian groups (Benjamin, 1972).Google Scholar
10.Kurosh, A. G., The theory of groups, Vol. 2 (Chelsea, 1956).Google Scholar
11.Lang, S., Rapport sur la cohomologie des groupes (Benjamin, 1966).Google Scholar
12.Leutbecher, A., Über Automorphiefaktoren und die Dedekindschen Summen, Glasgow Math. J. 11 (1970), 41–57.CrossRefGoogle Scholar
13.McKean, H. P., Selberg's trace formula as applied to a compact Riemann surface, Comm. Pure Appl. Math. XXV (1972), 225–246.CrossRefGoogle Scholar
14.Mumford, D., Abelian varieties (Oxford, 1970).Google Scholar
15.Narasimhan, M. S. and Seshadri, C. S., Stable and unitary vector bundles on a compact Riemann surface, Ann. Math. 82 (1965), 540–567.CrossRefGoogle Scholar
16.Petersson, H., Zur analytischen theorie der Grenzkreisgruppen, I., Math. Ann. 115 (1938), 23–67.CrossRefGoogle Scholar
17.Petersson, H., Zur analytischen theorie der Grenzkreisgruppen, III., Math. Ann. 115 (1938), 518–572.CrossRefGoogle Scholar
18.Roelcke, W., Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene, I, II, Math. Ann. 167 (1966), 292–337, Math. Ann. 168 (1967), 261–234.CrossRefGoogle Scholar
19.Selberg, A., Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. 20 (1956), 47–87.Google Scholar
20.Selberg, A., Discontinuous groups and harmonic analysis, Proc. Int. Cong. Math. (Stockholm, 1962), 177–189.Google Scholar
21.Selberg, A., On discontinuous groups in higher dimensional symmetric spaces. Contributions to Functions Theory (Bombay, 1960), 147–164.Google Scholar
22.Siegel, C. L., Über einige Ungleichungen bei Bewegungsgruppen in der nichteuklidischen Ebene, Math. Ann. 133 (1957), 127–138.CrossRefGoogle Scholar
23.Siegel, C. L., Analytische Zahlentheorie, II. Lecture notes (Wintersemester 1963/4, Göttingen).Google Scholar
24.Weil, A., Généralisation des fonctions abéliennes, J. Math. Pures et Appl. 17 (1938), 47–87.Google Scholar