Cohomology of Fuchsian Groups

Jump To References Section

Authors

  • P. K. Prasad
     School of Mathematics, Tata Institute of Fundamental Research, Colaba, Bombay 5 BR ,IN

Abstract

In his paper 'Remarks on the cohomology of groups' [11], Andre Weil computes the dimension of the space of cohomology classes of degree one given by parabolic cocycles of a group T acting discontinuously on the upper half plane H such that the quotient is compactifiable. In the particular case when T does not have fixed points in H and H/V is compact, this has also been done by M. S. Narasimhan and C. S. Seshadri in [6]. Whereas Weil used purely group-theoretic methods in his proof, the methods of [6] are based on the cohomology of local systems. The purpose of the present article is to give a proof of Weil's formula in the general case on the lines of [6] by using cohomology theory of sheaves. We make particular use of the Tohoku paper of Grothendieck [3], to which we shall refer in the sequel as 'Tohoku'.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

1974-12-01

How to Cite

Prasad, P. K. (1974). Cohomology of Fuchsian Groups. The Journal of the Indian Mathematical Society, 38(1-4), 51–63. Retrieved from http://informaticsjournals.com/index.php/jims/article/view/16681

Issue

Volume 38, Issue 1-4, March-December 1974

Section

Articles

License

Copyright (c) 1974 P. K. Prasad

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

H. CARTAM and S. EILENBERG, Homological Algebra, Princeton, University Press, 1956.

R. GODEMENT, Thiorie desfaisceaux, Hermann, Paris.

A. GROTHENDIECK, Sur quelques points d'algebre homologique, Tbhoku Mathematical Journal 2nd Ser. Vol. 9 (1957).

J. FRENKEL, Exp. 10, Coefficients Locaux, Seminaire Cartan, E. N. S. 1948–9.

J. LEHNER, A short course in automorphic functions, Holt, Rinehart & Winston.

M. S. NARASIMHAN and C. S. SESHADRI, Holomorphic vector bundles on a compact Riemann surface, Math. Annalen, 155(1964).

J. P. SERRE, Un theoreme de dualite, Comm. Math. Helv., Vol. 29 (1955).

C. S. SESHADRI, Generalised multiplicative meromorphic functions on a complex analytic manifold, J. Ind. Math. Soc. 21 (1957).

C. S. SESHADRI, Moduli of'n-vector bundles over an algebraic curve, Lectures at the Summer Institute, Varenna, 1969.

G. SPRINGER, Introduction to Riemann surface (Addison-Wesley).

A.WEIL, Remarks on the cohomology of groups, Annals of Mathematics, 80 (1964).