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Jul 21, 2016 at 14:03 comment added Dmitry Vaintrob Thanks Peter! This looks very much like what I'm looking for (and yes, the question comes from thinking about equivariant homotopy theory)
Jul 6, 2016 at 13:55 comment added Peter May Thanks Eric. Let me advertise a modernized exposition without full details: math.uchicago.edu/~may/PAPERS/Final1.pdf. But one caveat: it is not ``the'' $E_{\infty}$ operad. It is crucial to use two suitably related $E_{\infty}$ operads, and I wish I knew more such operad pairs than I do.
Jul 6, 2016 at 11:01 comment added Eric Peterson Chapter VII (and the beginning of Chapter VI) of May's LNM volume "$E_\infty$ Ring Spaces and $E_\infty$ Ring Spectra" is about doing exactly this: a recognition principle for connective $E_\infty$ ring spectra as spaces with two actions of the $E_\infty$ operad which distribute appropriately.
Jul 6, 2016 at 9:50 history asked Dmitry Vaintrob CC BY-SA 3.0