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

• 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?

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeApr 29th 2019

• 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…

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

• 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 $[\phi,\phi]_{Wh}$ (here).

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

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

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeApr 30th 2019

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

• 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). ]