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nLab > Latest Changes: Domenico: latest changes

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  1. Added Thom-Federer and Gottlieb thorems to Eilenberg-MacLane space; added the remark “ΩC(X,Y)≃C(X,ΩY)\Omega\mathbf{C}(X,Y)\simeq \mathbf{C}(X,\Omega Y) in any (oo,1)-category with homotopy pullbacks” in loop space object.

  2. created stub for Hodge star operator

  3. added a few remarks on Eilenberg-Mac Lane space and Whitehead tower.

    • CommentRowNumber4.
    • CommentAuthordomenico_fiorenza
    • CommentTimeJul 22nd 2010
    • (edited Jul 22nd 2010)

    at String Lie 2-algebra I guess CE(𝔰𝔱𝔯𝔦𝔫𝔤(n))=(∧ •𝔤 *⊕⟨b⟩,d 𝔰𝔱𝔯𝔦𝔫𝔤)CE(\mathfrak{string}(n))=(\wedge^\bullet\mathfrak{g}^*\oplus\langle b\rangle,d_\mathfrak{string}) should rather be

    CE(𝔰𝔱𝔯𝔦𝔫𝔤(n))=(∧ •(𝔤 *⊕⟨b⟩),d 𝔰𝔱𝔯𝔦𝔫𝔤)CE(\mathfrak{string}(n))=(\wedge^\bullet(\mathfrak{g}^*\oplus\langle b\rangle),d_\mathfrak{string}).

    waiting for feedback on this before editing the page.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2010

    Yes.

  6. ok, I’ll now edit that and add the explicit expression for the 3-brackets.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2010

    Thanks for taking care of that!

  8. done. when you have time, please check.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJul 22nd 2010
    • (edited Jul 22nd 2010)

    Thanks.

    I added a section on how 𝔰𝔱𝔯𝔦𝔫𝔤\mathfrak{string} is the b𝔲(1)\mathbf{b}\mathfrak{u}(1)-principal ∞\infty-bundle over 𝔰𝔬\mathfrak{so} classified by the cocycle μ:𝔰𝔬→b 2𝔲(1)\mu : \mathfrak{so} \to \mathbf{b}^2 \mathfrak{u}(1) .

  10. Leaving for two weeks: holiday :)

    Have a nice time,

    Domenico

  11. added a line just after equation (1) in group extension.

  12. Expanded coset.

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