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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 5th 2010
    • CommentRowNumber2.
    • CommentAuthorJohn Baez
    • CommentTimeDec 3rd 2016

    I talked to Chris Rogers today and I wound up trying to remember an amazing result by Mandell. I’ve added it to

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeDec 3rd 2016

    That paper is published. I fixed the link and added the publication data.

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeSep 4th 2019

    What is the reference that defines an E-infinity algebra structure on simplicial cochains C *(X,Z)C^*(X,Z) of a simplicial set XX?

    The article claims its existence, but does not give a reference.

    To be clear: such a structure can of course be quickly constructed using abstract machinery, but I am looking for a concrete description, with explicitly written down operations etc.

    • CommentRowNumber5.
    • CommentAuthorDylan Wilson
    • CommentTimeSep 4th 2019
    McClure-Smith (here: write down something very explicit for singular cochains on a space, and at first glance it doesn't seem like they use anything very special about it coming from a space (i.e. it ought to work for cochains on a simplicial set). Their other paper also seems relevant:
    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeSep 5th 2019

    Added a description of the McClure-Smith paper.

    diff, v9, current

    • CommentRowNumber7.
    • CommentAuthorDmitri Pavlov
    • CommentTimeSep 5th 2019
    • (edited Sep 5th 2019)

    Thanks a lot, this is exactly what I was looking for. They do not seem to use anything specific to singular cochains; the operations involved generalize the cup product and Steenrod’s cup-i products, and are naturally defined for simplicial cochains.

    I added a description of their work to the main article.

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeSep 6th 2019
    • (edited Sep 6th 2019)
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