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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 $C^*(X,Z)$ of a simplicial set $X$?

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: https://arxiv.org/pdf/math/0106024.pdf) 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: https://arxiv.org/pdf/math/0211368.pdf.
• CommentRowNumber6.
• CommentAuthorDmitri Pavlov
• CommentTimeSep 5th 2019

Added a description of the McClure-Smith paper.

• 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)