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Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
High Energy Physics - Theory · Submitted 21 Jan 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This provides another confirmation that cohomotopy is the proper generalized cohomology theory to describe these fields.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We compare the description of the M-theory form fields via cohomotopy versus that via integral cohomology. | contribution 0.86 | 0.81 | 0.07 | asserted 0.79 |
| s1 | 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. | method 0.45 | 0.85 | 0.11 | asserted 1.00 |
| s2 | 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. | result 0.83 | 0.92 | 0.35 | asserted 0.99 |
| s3 | Bringing in the geometry leads to a differential refinement of the Postnikov tower, which should be of independent interest. | contribution 0.78 | 0.82 | 0.08 | asserted 0.61 |
| s4 | This provides another confirmation that cohomotopy is the proper generalized cohomology theory to describe these fields. | interpretation 0.98 | 0.74 | 0.65 | asserted 0.86 |
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The paper
Original 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.
Human review
How the literature uses it
10 arXiv papers cite this in 20 sentences
Papers citing it · 17 sentences without a confident label
Cites it as background 3 papers
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Now the (twisted) generalized cohomology theory classified by the (quaternionic Hopf fibration between) spheres is called (twisted, unstable) co-Homotopy theory (review and pointers in [ref] , more on this in <ref> below), denoted as follows: [equation] Therefore, the hypothesis that this “evident” choice of flux-quantization is the “correct” one for completing the theory of the M5-brane in M-theory has been called “Hypothesis H” in [ref] [ref] [ref] [ref] [ref] , following [ref] (the corresponding differential co-Homotopy for the M5-brane fields was first considered in [ref] ), which may be thought of as an M-theoretic version of the traditional “Hypothesis K” that D-brane charges are in (twisted) K-theory (cf. [ref] ).
Flux Quantization on M5-branes · Introduction and Overview · 0.81
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[ The issue of promoting $L_∞$-algebra valued flux densities as in [ref] to globally defined higher gauge fields is the topic of flux quantization [ref] [ref] [ref] by which more subtle topological aspects of M-theory are resolved [ref] [ref] [ref] . ]
Super-$\mathrm{Lie}_\infty$ T-Duality and M-Theory · Introduction & Overview · 0.81
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Of particular note is “hypothesis H” of Fiorenza–Sati–Schreiber [ref] proposing that the $C$-field in M-theory is quantized using twisted differential cohomotopy; work of Fiorenza, Sati, Schreiber, and their collaborators [ref] , as well as Roberts [ref] , explores this hypothesis and its consequences.
Differential cohomology (encyclopedia article) · Quantizing in more general cohomology theories · 0.82
What it cites · 61 sentences without a confident label
Compares with 4 papers
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[ref] reproduces the correct mod 2 congruence condition for $G_4^form∧G_4^form$, previously obtained using $E_8$-gauge theory in [ref] .
On Flux Quantization In M-Theory And The Effective Action · Differential cohomotopy vs. differential cohomology · 0.98
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Namely, we have the condition [equation] As indicated above, this is compatible with [ref] , where a similar condition was proposed using Spin K-theory.
An approach to anomalies in M-theory via KSpin · $$ coefficients · 0.89
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[Obstructions via refinement of cohomology operations] Consider the refinement of the Steenrod square $Sq^2$, given by the composition [ref] [equation] This is almost, but not quite, the differential refinement of $Sq^3$ discussed in [ref] .
Primary operations in differential cohomology · Torsion obstructions in differential cohomology · 0.88
Cites as support 1 paper
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The first obstruction is [By “$!=$", we mean that we require the equality, but also that this does not necessarily automatically hold.] [equation] Indeed, it was shown in [ref] that this follows from anomaly cancellation in M-theory.
Twisted Cohomotopy implies M-theory anomaly cancellation on 8-manifolds · Identifying the obstruction classes · 1.00
Cites as background 21 papers
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𝐁^3U(1)_∇ . where $S^4$ is the differential refinement of the 4-sphere (see [ref] [ref] [ref] for complementary approaches) and $𝐁^3U(1)_∇$ is the smooth stack of 3-bundles with connections (see [ref] [ref] [ref] [ref] [ref] ).
Extended higher cup-product Chern-Simons theories · Introduction · 0.84
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𝐁^3U(1)_∇ . where $S^4$ is the differential refinement of the 4-sphere (see [ref] [ref] [ref] for complementary approaches) and $𝐁^3U(1)_∇$ is the smooth stack of 3-bundles with connections (see [ref] [ref] [ref] [ref] [ref] ).
A higher stacky perspective on Chern-Simons theory · Introduction · 0.84
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𝐁^3U(1)_∇ . where $S^4$ is the differential refinement of the 4-sphere (see [ref] [ref] [ref] for complementary approaches) and $𝐁^3U(1)_∇$ is the smooth stack of 3-bundles with connections (see [ref] [ref] [ref] [ref] [ref] ).
Differential cohomology in a cohesive infinity-topos · Introduction · 0.84
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