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nLab > Latest Changes: iterated loop space

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 6th 2019

    started a Properties-section, with material copied from other entries:

    1. the rational cohomology of iterated loop spaces of spheres

    2. the relation to configuration spaces of points

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 10th 2020

    added ISBN and DOI to:

    diff, v8, current

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeSep 10th 2020
    • (edited Sep 10th 2020)

    I changed John Adams (who I had never heard of) to John Frank Adams (i.e. Frank Adams) I only ever heard him called Frank Adams, and the ‘Frank’ should be visible in the citation.

    diff, v9, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 1st 2021
    • (edited Oct 1st 2021)

    added a section (here) with discussion of the homotopy fiber sequence

    Ω nA→hofib(ev *)Maps(ʃS n,A)→ev *A \Omega^n A \xrightarrow{ hofib(ev_{\ast}) } Maps \big( ʃ S^n ,\, A \big) \xrightarrow{ ev_\ast } A

    and the observation that

    τ n(A)≃AAAAAA⇒AAAAAMaps(ʃS n+2,A)⟶∈W whev *A. \tau_{n}(A) \,\simeq\, A {\phantom{AAAAA}} \Rightarrow {\phantom{AAAAA}} Maps \big( ʃ S^{n+2} ,\, A \big) \underoverset {\in \mathrm{W}_{wh}} {ev_\ast} {\longrightarrow} A \,.

    This should maybe rather go to an entry “free higher loop space” or similar, but since that doesn’t exist (yet), I’ll keep it here, for the time being.

    diff, v11, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 21st 2021

    added pointer to:

    diff, v12, current

1 to 5 of 5

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