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Homotopy theory, homological algebra, algebraic treatments of manifolds.
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Module structure of $\Omega_*(Z_p)$
In Conner-Floyd's book, Differentiable Periodic Maps in (46.1), for p an odd prime and $k=1,2,\dots$, it is posted the identities:
$$p\alpha_{2k+1}+[M^4]\alpha_{2k-3}+[M^8]\alpha_{2k-7}+\dots=0$$
in $ …