While it is well-known that the charges of F1/Dp-branes in type II string theory need to be refined from de Rham cohomology to certain twisted generalized differential cohomology theories, it is an open problem to determine the generalized cohomology theory for M2-brane/M5-branes in 11 dimensions. I discuss how a careful re-analysis of the old brane scan (arXiv:1308.5264 , arXiv:1506.07557, joint with Fiorenza and Sati) shows that rationally and unstably, the M2/M5 brane charge is in degree-4 cohomotopy. While this does not integrate to the generalized cohomology theory called stable cohomotopy, it does integrate to GG-equivariant stable cohomotopy, for GG a non-cyclic finite group of ADE type. On general grounds, such an equivariant cohomology theory needs to be evaluated on manifolds with ADE orbifold singularities, and picks up contributions from the orbifold fixed points. Both of these statements are key in the hypothesized but open problem of gauge enhancement in M/F-theory.

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