A 3-Dimensional Non-Abelian Cohomology of Groups With Applications to Homotopy Classification of Continuous Maps

Abstract

The general problem of what should be a non-abelian cohomology, what is it supposed to do, and what should be the coefficients, form a set of interesting questions which has been around for a long time. In the particular setting of groups, a comprehensible and well motivated cohomology theory has been so far stated in dimensions ≤ 2, the coefficients for being crossed modules. The main effort to define an appropriate for groups has been done by Dedecker [16] and Van Deuren [40]; they studied the obstruction to lifting non-abelian 2-cocycles and concluded with first approach for , which requires “super crossed groups” as coefficients. However, as Dedecker said “some polishing work remains necessary” for his cohomology.