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nLab > Latest Changes: twisting function

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  1.  
    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeNov 28th 2023
    • (edited Nov 28th 2023)

    I corrected the ’historical’ comment. The Cartan seminar is December 1956 and E. H. Brown’s paper was submitted in 1958 so essentially the two theories were developed in tandem.

    diff, v13, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2023

    After streamlining the paragraph with your edit (here), it reads:

    Twisting functions are the analogue of twisting cochains in the context of simplicial sets; twisting cochains were introduced by Brown 1959, whilst twisting functions were discussed in Cartan 1956.

    which seems to confirm the original wording. No?

    diff, v14, current

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeNov 28th 2023
    • (edited Nov 28th 2023)

    I am not too bothered, but as I read it, without the dates ,the implication seemed to be that Brown preceeded Cartan. Just out of interest, I noticed that the twisted cartesian product is also mentioned in John Moore’s 1956 seminar from Princeton. John Moore’s notes get quite near E. H. Brown’s work. Was E.H. Brown at Princeton during that time? I don’t know.

    BTW Cartan’s exposé in his seminar is very nicely written and is possibly clearer than later discussions, although that is just probably my preference for quite explicit calculations showing through!

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeNov 28th 2023

    Tim, the original formulation of that line was also due to you (revision 3 in 2009) and I think at the beginning of the sentence you had the right idea but it got obscured a bit by the ambiguous ending of the sentence.

    • CommentRowNumber5.
    • CommentAuthorTim_Porter
    • CommentTimeNov 28th 2023
    • (edited Nov 28th 2023)

    Quite possibly. I often look back on wording I have used and ask myself why on earth I put it in that form! Such is life. I also had not quite worked out which came first, and thought I had seen someone claim that the cochain case came before the twisting function.

    I have not checked up if Brown refers to twisting functions. I do not have a ready copy of his paper.

1 to 5 of 5

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