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: Hurewicz theorem

Bottom of Page

1 to 16 of 16

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 10th 2011

    created placeholder for Hurewicz theorem

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeOct 10th 2011
    • (edited Oct 10th 2011)

    I have created several entries today, under construction, and will report more on that in few days, when having time, some are such stubs and some have some real material like Selberg integral.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 22nd 2012
    • (edited Aug 31st 2012)

    noticed that Hurewicz theorem was still empty, and briefly added the statement

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeAug 31st 2012

    added to Hurewicz theorem the definition of the Hurewicz homomorphism.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeSep 22nd 2018

    added paragraph (here) indicating the stable version and its generalization to the Boardman homomorphism

    diff, v13, current

    • CommentRowNumber6.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 21st 2022

    Added:

    The original reference is

    • Witold Hurewicz, _Beitrage zur Topologie der Deformationen), Neder. Akad. Wetensch. 38 (1935), 521–528.

    The simplicial version is due to

    • Daniel M. Kan, The Hurewicz theorem, 1958 Symposium internacional de topología algebraica (International symposium on algebraic topology), pp. 225–231 Universidad Nacional Autónoma de México and UNESCO, Mexico City.

    diff, v20, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 21st 2022
    • (edited May 21st 2022)

    thanks. is there any online trace of Beiträge zur Topologie der Deformationen? I only see it listed on gbooks, where however no content is visible either

    diff, v21, current

    • CommentRowNumber8.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 22nd 2022

    Re #7: The article is reproduced in its entirety in “Collected Works of Witold Hurewicz”, a book that is available online in Library Genesis.

    Here is a full citation:

    Koninklijke Akademie van Wetenschappen: Proceedings of the Section of Sciences 38 (1935), 112–119.

    Mathematics. — Beiträge zur Topologie der Deformationen (l. Höherdimensionale Homotopiegruppen).

    By Dr. W. Hurewicz

    (Communicated by Prof. L. E. J. Brouwer).

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeMay 22nd 2022

    Right, I should have been more explicit: I am looking for useful hyperlinks that we could provide with the reference item on the nLab page. I guess we dont want to link to Library Genesis from nLab pages to avoid legal trouble.(?) At least thats what I used to not do.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMay 22nd 2022

    I noticed that the section stating the actual theorem (here) did not mention the cases in degree ≤1\leq 1. I have now filled that in by essentially copying over the two Propositions to this extent that we did have all along at singular homology.

    Also added a kind of Idea-paragraph to before these statements (still here)

    diff, v22, current

    • CommentRowNumber11.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 22nd 2022

    Added:

    This article is reproduced on pages 341–348 of

    diff, v23, current

    • CommentRowNumber12.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 22nd 2022
    • (edited May 22nd 2022)

    Re #9: I think supplying the book name is sufficient, which is what I just did. Everybody knows where to look for books these days. These Google Books links are now quite useless, by the way: it is virtually impossible to look inside. (This used to be quite different 10 years ago or so.)

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeMay 22nd 2022

    Okay, sounds good.

    Sure, GoogleBooks rarely shows content these days, but in the absence of any published page for a reference, it is at least a kind of online proof of existence.

    (Incidentally, some GBooks look inaccessible but do still open up as soon as one uses the “search inside” functionality. Not though in this case, unfortunately.)

    • CommentRowNumber14.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 23rd 2022

    Added a direct link for the official digitized PDF of Hurewicz’s paper in the open digital archive of Indagationes Mathematicae.

    diff, v24, current

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeMay 23rd 2022

    ah, great, thanks!

    I have also updated the link here

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeJul 25th 2024
    • (edited Jul 25th 2024)

    The page used to claim that the Hurewicz theorem is due to (after reformatting):

    • Witold Hurewicz: Beiträge zur Topologie der Deformationen (I. Höherdimensionale Homotopiegruppen), Proc. Akad. Wet. Amsterdam 38 (1935) 112–119 [pdf]

    but I suppose it is really due to part II:

    • Witold Hurewicz: Beiträge zur Topologie der Deformationen (II. Homotopie- und Homologigruppen), Proc. Akad. Wet. Amsterdam 38 (1935) 521–528 [pdf]

    I have fixed this here and instead am adding pointer to part I above at homotopy group.

    diff, v27, current

1 to 16 of 16

  1.