Not signed in (Sign In)

Not signed in

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

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: twisting function

Bottom of Page

1 to 5 of 5

  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

  1.