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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeOct 6th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarted 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 <a href="https://ncatlab.org/nlab/revision/diff/iterated+loop+space/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/iterated+loop+space/4">v4</a>, <a href="https://ncatlab.org/nlab/show/iterated+loop+space">current</a>

   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

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 10th 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded ISBN and DOI to: * [[John Adams]], _Infinite loop spaces_, Herrmann Weyl lectures at IAS, Princeton University Press (1978) ([ISBN:9780691082066](https://press.princeton.edu/books/paperback/9780691082066/infinite-loop-spaces-am-90-volume-90), [doi:10.1515/9781400821259](https://doi.org/10.1515/9781400821259)) <a href="https://ncatlab.org/nlab/revision/diff/iterated+loop+space/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/iterated+loop+space/8">v8</a>, <a href="https://ncatlab.org/nlab/show/iterated+loop+space">current</a>

   added ISBN and DOI to:

   • John Adams, Infinite loop spaces, Herrmann Weyl lectures at IAS, Princeton University Press (1978) (ISBN:9780691082066, doi:10.1515/9781400821259)

   diff, v8, current

3. • CommentRowNumber3.
   • CommentAuthorTim_Porter
   • CommentTimeSep 10th 2020
   • (edited Sep 10th 2020)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexI 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. <a href="https://ncatlab.org/nlab/revision/diff/iterated+loop+space/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/iterated+loop+space/9">v9</a>, <a href="https://ncatlab.org/nlab/show/iterated+loop+space">current</a>

   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

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeOct 1st 2021
   • (edited Oct 1st 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a section ([here](https://ncatlab.org/nlab/show/iterated+loop+space#Homotopy)) with discussion of the homotopy fiber sequence $$ \Omega^n A \xrightarrow{ hofib(ev_{\ast}) } Maps \big( &#643; S^n ,\, A \big) \xrightarrow{ ev_\ast } A $$ and the observation that $$ \tau_{n}(A) \,\simeq\, A {\phantom{AAAAA}} \Rightarrow {\phantom{AAAAA}} Maps \big( &#643; S^{n+2} ,\, A \big) \underoverset {\in \mathrm{W}_{wh}} {ev_\ast} {\longrightarrow} A \,. $$ 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. <a href="https://ncatlab.org/nlab/revision/diff/iterated+loop+space/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/iterated+loop+space/11">v11</a>, <a href="https://ncatlab.org/nlab/show/iterated+loop+space">current</a>

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

   and the observation that

   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

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeDec 21st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Douglas Ravenel]], *What we still don't know about loop spaces of spheres*, in: [[Mark Mahowald]], [[Stewart Priddy]] (eds.), *Homotopy Theory via Algebraic Geometry and Group Representations*, Contemporary Mathematics **220** (1998) ([pdf](https://people.math.rochester.edu/faculty/doug/mypapers/loop.pdf), [doi:10.1090/conm/220](http://dx.doi.org/10.1090/conm/220)) <a href="https://ncatlab.org/nlab/revision/diff/iterated+loop+space/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/iterated+loop+space/12">v12</a>, <a href="https://ncatlab.org/nlab/show/iterated+loop+space">current</a>

   added pointer to:

   • Douglas Ravenel, What we still don’t know about loop spaces of spheres, in: Mark Mahowald, Stewart Priddy (eds.), Homotopy Theory via Algebraic Geometry and Group Representations, Contemporary Mathematics 220 (1998) (pdf, doi:10.1090/conm/220)

   diff, v12, current