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A citation to "M. J. Hopkins and P. Goerss, Multiplicative stable homotopy theory, unpublished manuscript, 1996" appears in the Hill, Hopkins, Ravenel Annals paper on the Kervaire invariant. It was also cited as "book in preparation" in the Hopkins-Singer paper on Quadratic Functions. And, it was cited by Goerss-Hopkins "Realizing commutative ring spectra as $E_\infty$ spectra" (which, I think, was later subsumed by "Moduli spaces of commutative ring spectra"). This last citation also cites a preprint by the same authors called "Resolutions in model categories" and another called "Simplicial structured ring spectra."

Clearly, this "Multiplicative stable homotopy theory" manuscript contained a lot of important ideas. I would like to know if a draft of it was ever posted online, or if it eventually appeared under a different name, or if another paper ever came along and subsumed it. I'm also curious about the status of the other two preprints by Goerss and Hopkins that I mentioned above.

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  • $\begingroup$ At the bottom of Goerss' webpage are links to a bunch of manuscripts under the header "The Multiplicative Ring Spectra Project, with Mike Hopkins". I think these are supposed to (mostly) comprise the "Multiplicative stable homotopy theory" manuscript, but I'm not Goerss or Hopkins, so I can't say for sure. $\endgroup$
    – skd
    Commented Sep 14, 2018 at 1:45
  • $\begingroup$ Thanks, but I don't think that's it. The only one on Goerss's webpage that seems to match the papers listed above is the Moduli spaces one. But, if that one had already subsumed the "multiplicative stable homotopy theory" one then I feel like Hopkins wouldn't still be citing the latter in 2005 and 2016 $\endgroup$
    – David White
    Commented Sep 14, 2018 at 1:53
  • $\begingroup$ That's true, yeah. $\endgroup$
    – skd
    Commented Sep 14, 2018 at 2:00
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    $\begingroup$ I suspect strongly that it was not released publicly; I've never seen it and it's in my wheelhouse. Since it dates back to a period when EKMM and Hovey-Shipley-Smith were just coming out, and since some of the references indicate it specifically for definitions of spectra, I might hazard a guess that some of the material was foundational in nature and became unneeded. I would almost certainly guess that many of these ideas appear in "Moduli spaces of commutative ring spectra" and the unpublished-but-available "Moduli problems for structured ring spectra". $\endgroup$
    – Tyler Lawson
    Commented Sep 14, 2018 at 10:34
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    $\begingroup$ As a general note: you probably shouldn't always take titles of unpublished manuscripts very seriously. Especially for documents which are far away from publication, such titles are likely to evolve over time, and can sometimes seem to exist in an uncertain quantum state, taking a different form every time it is observed. $\endgroup$
    – Charles Rezk
    Commented Sep 14, 2018 at 13:58

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