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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'.

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'.

FGRAAL is a FORTRAN-based graph algorithmic compiler language designed for use in the solution of applied graph problems. This report describes a number of UNIVAC 1108 routines which analyze the topological structure of directed and undirected graphs, including induced subgraphs, spanning trees, connected and strong components, fundamental cycles and cocycles, and blocks. In addition, several utility procedures and input/output routines are described, as well as a random graph generator.