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

Published online by Cambridge University Press:  20 November 2018

Manuel Bullejos
Departamento de Algebra, Facultadde Ciencias, University of Granada, Granada 18075, Spain.
Antonio M. Cegarra
Departamento de Algebra, Facultadde Ciencias, University of Granada, Granada 18075, Spain.
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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.

Research Article
Copyright © Canadian Mathematical Society 1991


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