The problem of finding topological properties of manifolds given analytically, geometrically or in some other way is very important for the topology itself as well as for its applications. In so general a formulation this problem seems to be somewhat indeterminate, since it is not quite clear precisely which manifolds are meant. For its solution in each concrete case it is necessary to point out explicitly which type of manifolds is to be considered and which topological properties are asked for. É. Cartan has proposed as such a concrete problem the question on the homological invariants of group spaces and homogeneous spaces closely connected with them. He developed a general method of dealing with this question consisting in the study of certain skew-symmetrical forms and thus transposed a geometrical question into the domain of pure algebra [1]. Cartan’s method yielded, however, so far comparatively few results, since the arising algebraical problems are of considerable difficulty.