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

Abstract

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 is 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.

30 pages, minor corrections and improvements, to appear in Journal of Geometry and Physics

References in corpus (4)

• Higher Topos Theory
• The M-theory 3-form and E8 gauge theory
• The Rational Higher Structure of M-theory
• An approach to anomalies in M-theory via KSpin

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• Flux Quantization on M5-branes
• Rational Homotopy Theory
• Anyons on M5-Probes of Seifert 3-Orbifolds via Flux Quantization
• Engineering of Anyons on M5-Probes via Flux Quantization
• Differential cohomology (encyclopedia article)
• Mysterious Triality and the Exceptional Symmetry of Loop Spaces