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We compare the description of the M-theory form fields via cohomotopy versusthat via integral cohomology. The conditions for lifting the latter to theformer are identified using obstruction theory in the form of Postnikov towers,where torsion plays a central role. A subset of these conditions is shown tocorrespond compatibly to existing consistency conditions, while the rest arenew and point to further consistency requirements for M-theory. Bringing in thegeometry leads to a differential refinement of the Postnikov tower, whichshould be of independent interest. This provides another confirmation thatcohomotopy is the proper generalized cohomology theory to describe thesefields.

Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers