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

我们通过同伦对与同位同伦对M理论形式域的描述进行了比较。使用障碍理论以Postnikov塔的形式确定了将后者提升到前者的条件，其中扭力起着核心作用。这些条件的一个子集显示为与现有的一致性条件兼容，而其余的则是新的，并指出了M理论的进一步一致性要求。引入几何形状会导致Postnikov塔的差异化改进，这应该是与众不同的。这再次证明了同伦是描述这些领域的适当的广义同伦理论。