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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 29th 2019

    started adding something (the example of the Hopf fibration and some references).

    What’s a canonical reference on the Whitehead products corresponding to the Hopf fibrations? Like what is an original reference and what is a textbook account?

    diff, v11, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 29th 2019

    added more references on Whitehead products in rational homotopy theory, here

    diff, v12, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 30th 2019

    I have added a section Relation to Sullivan models with the statement that the co-binary part of the Sullivan differential equals the \mathbb{Q}-linear dual of the Whitehead product.

    There is a hidden factor of 2 in that statement, which I would like to understand better. But I’ll give that statement now it’s own entry, and then ask my question there…

    diff, v13, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 30th 2019
    • (edited Apr 30th 2019)

    finally added the original references

    • J. H. C. Whitehead, Section 3 of On Adding Relations to Homotopy Groups, Annals of Mathematics Second Series, Vol. 42, No. 2 (Apr., 1941), pp. 409-428 (jstor:1968907)

    Then I made explicit the subtlety with [ϕ,ϕ] Wh[\phi,\phi]_{Wh} (here).

    Finally I reorganized a little, starting to put the previous material into appropriate subsections.

    diff, v14, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 30th 2019
    • (edited Apr 30th 2019)

    made the shift in the grading more explicit

    diff, v14, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 30th 2019

    added the actual definition;

    moved all discusson of super Lie algebra structure to the Properties-section

    diff, v14, current

    • CommentRowNumber7.
    • CommentAuthorGuest
    • CommentTimeSep 14th 2020
    The commutativity statement appears to be wrong. On the LHS and RHS you have phi_1 and phi_2 in the same order. The sign in front of them appears to be wrong, as well. It should be (-1)^{n_1n_2}. The proof is rather elementary, and boils down to the linear iso of R^{n_1+n_2} that switches the first n_1 columns with the last n_2 has determinant (-1)^{n_1n_2}. -Ryan Budney
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeSep 15th 2020
    • (edited Sep 15th 2020)

    Thanks for catching this. Both fixed now.

    [ The missing re-ordering was a silly typo, but the difference in sign came from thinking L-infinity algebras as opposed to dg-Lie algebras, via the pertinent isomorphism (equation (3) in arXiv:hep-th/9209099). ]

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