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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 20th 2016
    • (edited Jan 20th 2016)

    I have been making trivial edits (adding references, basic statements, cross-links ) to Hopf invariant and a bunch of related entries, such as Kervaire invariant, Hopf invariant one problem, Arf-Kervaire invariant problem, normed division algebra.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2019

    added these pointer:

    Discussion via differential forms/rational homotopy theory

    • J. H. C. Whitehead, An expression of Hopf ’s invariant as an integral, Proc. Nat. Acad. Sci. U. S. A.33 (1947), 117–123 (jstor:87688)

    • Dev Sinha, Ben Walter, Lie coalgebras and rational homotopy theory II: Hopf invariants (arXiv:0809.5084)

    diff, v11, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 26th 2019

    and this one:

    • André Haefliger, p. 3 of Whitehead products and differential forms, In: Schweitzer P.A. (eds) Differential Topology, Foliations and Gelfand-Fuks Cohomology. Lecture Notes in Mathematics, vol 652. Springer, Berlin, Heidelberg (doi:10.1007/BFb0063500)

    diff, v11, current

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 26th 2019

    If at the beginning the requirement is n>1n \gt 1 in ϕ:S 2n1S n\phi \;\colon\; S^{2n-1} \longrightarrow S^n, then I guess the real Hopf fibration shouldn’t be included.

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 26th 2019

    Mind you, Adams and Atiyah allow that case, so presumably change to n>0n \gt 0.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 29th 2019

    added pointer to

    • Dale Husemöller, chapter 15 of Fibre Bundles, Graduate Texts in Mathematics 20, Springer New York (1966)

    diff, v12, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 21st 2019

    added publication data for this here:

    diff, v13, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 30th 2019

    added pointer to

    diff, v14, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJun 3rd 2019
    • (edited Jun 3rd 2019)

    added the claim (here) that the Hopf invariant of a map ϕ\phi may be read off as the unique free coefficient of the Sullivan model of ϕ\phi.

    This follows straightforwardly, and I’d like to cite this from a canonical RHT source, if possible. But I don’t see it in the textbooks (FHT, …). If anyone knows opus, page and verse for a canonical citation of this fact, please let me know.

    diff, v16, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 4th 2019

    added also pointer to

    diff, v18, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 5th 2019

    added also pointer to


    • Lee Rudolph, Whitehead’s Integral Formula, Isolated Critical Points, and the Enhancement of the Milnor Number, Pure and Applied Mathematics Quarterly Volume 6, Number 2, 2010 (arXiv:0912.4974)

    diff, v19, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2019

    added pointer to

    diff, v22, current

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