Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Forgot your password?
• Apply for membership

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 5th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub for [[E-infinity algebra]]

   stub for E-infinity algebra

2. • CommentRowNumber2.
   • CommentAuthorJohn Baez
   • CommentTimeDec 3rd 2016
   • PermaLink
   Author: John Baez
   Format: MarkdownItexI talked to Chris Rogers today and I wound up trying to remember an amazing result by Mandell. I've added it to * [[E-infinity+algebra#in_chain_complexes|E-infinity algebras: in chain complexes]].

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

   • E-infinity algebras: in chain complexes.
3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeDec 3rd 2016
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexThat paper is published. I fixed the link and added the publication data.

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

4. • CommentRowNumber4.
   • CommentAuthorDmitri Pavlov
   • CommentTimeSep 4th 2019
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexWhat 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.

   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.

5. • CommentRowNumber5.
   • CommentAuthorDylan Wilson
   • CommentTimeSep 4th 2019
   • PermaLink
   Author: Dylan Wilson
   Format: TextMcClure-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.

   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.
6. • CommentRowNumber6.
   • CommentAuthorDmitri Pavlov
   • CommentTimeSep 5th 2019
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded a description of the McClure-Smith paper. <a href="https://ncatlab.org/nlab/revision/diff/E-infinity+algebra/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/E-infinity+algebra/9">v9</a>, <a href="https://ncatlab.org/nlab/show/E-infinity+algebra">current</a>

   Added a description of the McClure-Smith paper.

   diff, v9, current

7. • CommentRowNumber7.
   • CommentAuthorDmitri Pavlov
   • CommentTimeSep 5th 2019
   • (edited Sep 5th 2019)
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexThanks 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.

   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.

8. • CommentRowNumber8.
   • CommentAuthorDmitri Pavlov
   • CommentTimeSep 6th 2019
   • (edited Sep 6th 2019)
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAlso discussed by Tyler Lawson here: <https://mathoverflow.net/questions/280627/is-the-e-infty-structure-on-the-cochain-complex-of-a-kg-n-readily-underst/281697#281697>

   Also discussed by Tyler Lawson here: https://mathoverflow.net/questions/280627/is-the-e-infty-structure-on-the-cochain-complex-of-a-kg-n-readily-underst/281697#281697

9. • CommentRowNumber9.
   • CommentAuthorHurkyl
   • CommentTimeOct 24th 2023
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexShould the contents of [[commutative monoid in a symmetric monoidal (infinity,1)-category]] be merged into this page? (that other page doesn't even have a 'discuss' page)

   Should the contents of commutative monoid in a symmetric monoidal (infinity,1)-category be merged into this page?

   (that other page doesn’t even have a ’discuss’ page)

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeOct 24th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded the requirement that $C$ be stable to justify saying "$E_\infty$-algebras" for these $E_\infty$-monoids. <a href="https://ncatlab.org/nlab/revision/diff/E-infinity+algebra/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/E-infinity+algebra/11">v11</a>, <a href="https://ncatlab.org/nlab/show/E-infinity+algebra">current</a>

    added the requirement that $C$ be stable to justify saying “$E_\infty$-algebras” for these $E_\infty$-monoids.

    diff, v11, current