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• 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

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeSep 10th 2020

• 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.

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

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

$\Omega^n A \xrightarrow{ hofib(ev_{\ast}) } Maps \big( ʃ S^n ,\, A \big) \xrightarrow{ ev_\ast } A$

and the observation that

$\tau_{n}(A) \,\simeq\, A {\phantom{AAAAA}} \Rightarrow {\phantom{AAAAA}} Maps \big( ʃ S^{n+2} ,\, A \big) \underoverset {\in \mathrm{W}_{wh}} {ev_\ast} {\longrightarrow} A \,.$

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.