Cohomology Theory with Higher Coboundary Operators I. (Construction of the Groups).

摘要

The purpose of the present work is to give a generalization of the classical cohomology theory in algebraic topology by introducing coboundary operators of higher order. In the present note, we shall construct such a theory in details by using WALLACE cochains of a topological space. However, one might easily establish analogous generalisations for the singular homology and cohomology theory and for the homology and cohomology groups of an abstract group. (AN).