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Oct 14, 2016 at 12:29 comment added Sean Tilson There is a recasting in the $H_{\infty}$-ring spectra book in chapter 4 that may be helpful. Also, chapter 4 of Bruner's Adams spectral sequence primer may be helpful.
Oct 13, 2016 at 23:19 comment added Anton Kapustin I have looked at May's paper, but did not find a cochain-level proof of Cartan's formula. I did find there a reference to an interesting paper by G. Hirsch "Quelques proprietes des produits de Steenrod" (1955). Hirsch proves that for any $x$, $a\mapsto a\cup_1 x$ is a derivation of the algebra of mod-2 cochains, but he does not say anything about higher cup products.
Oct 13, 2016 at 16:36 history edited David C CC BY-SA 3.0
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Oct 13, 2016 at 10:30 history edited David C CC BY-SA 3.0
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Oct 13, 2016 at 6:12 history answered David C CC BY-SA 3.0