Differential cohomotopy versus differential cohomology for Mtheory and differential lifts of Postnikov towers
Abstract
We compare the description of the Mtheory 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 Mtheory. 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.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 July 2021
 DOI:
 10.1016/j.geomphys.2021.104203
 arXiv:
 arXiv:2001.07640
 Bibcode:
 2021JGP...16504203G
 Keywords:

 Mtheory;
 Differential cohomology;
 Postnikov towers;
 Flux quantization;
 Cohomology operations;
 Hypothesis H;
 High Energy Physics  Theory;
 Mathematics  Algebraic Topology
 EPrint:
 30 pages, minor corrections and improvements, to appear in Journal of Geometry and Physics