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Since Hisham’s article came out
I briefly created a stub entry ninebrane structure and expanded the higher spin structure - table accordingly. More should be done here, but I don’t have the leisure right now.
You may not have the time now, but for later: if the tangent bundle of an 11-manifold has a classifying map that lifts to the 13-connected cover of BO(11), then isn’t the tangent bundle trivialisable?
Yes, but the space of choices of ninebrane structures may still be non-trivial and, maybe more importantly, after differential refinement the secondary invariants are non-trivial, they are the 11d Chern-Simons invariants.
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