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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMar 4th 2019

Page created, but author did not leave any comments.

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMar 4th 2019
• (edited Mar 4th 2019)

some minimum, for the moment just so as to record the fact that

$Maps_f\big( S^n, S^n\big) \;\simeq_{\mathbb{Q}}\; \left\{ \array{ S^n \times S^{n-1} &\vert& n\,\text{even}\,, deg(f) = 0 \\ S^{2n-1} &\vert& n \, \text{even}\,, deg(f) \neq 0 \\ S^n &\vert& n\, \text{odd} } \right.$
• CommentRowNumber3.
• CommentAuthorTodd_Trimble
• CommentTimeMar 4th 2019

Something seems missing. Should the third line include the condition $deg(f) = 0$? Because we can’t have both $n\; odd, deg(f) \neq 0 \Rightarrow n\; odd \Rightarrow Maps_f(S^n, S^n) \simeq_\mathbb{Q} S^n$ and $n\; odd, deg(f) \neq 0 \Rightarrow Maps_f(S^n, S^n) \simeq_\mathbb{Q} S^{2n-1}$.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeMar 4th 2019
• (edited Mar 4th 2019)

Thanks for catching this. The first “odd” should have been the second “even”. Fixed now.

• CommentRowNumber5.
• CommentAuthorDavidRoberts
• CommentTimeMar 5th 2019

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeMar 5th 2019

Thanks.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeSep 12th 2019
• (edited Sep 12th 2019)

• Samuel B. Smith, A based Federer spectral sequence and the rational homotopy of function spaces, Manuscripta Math (1997) 93: 59 (doi:10.1007/BF02677458)

based on

• Herbert Federer, A Study of Function Spaces by Spectral Sequences, Transactions of the American Mathematical Society Vol. 82, No. 2 (Jul., 1956), pp. 340-361 (jstor:1993052)
• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeOct 6th 2019

added statement of the rational cohomology of $\Omega^D S^n$, for $1 \leq D \lt n = 2k$ (here)

am adding this statement also to iterated loop space

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeOct 7th 2019

added a bunch of further references

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTime4 days ago

Corrected a mistake in the discussion of the rational model for $\Omega^D S^D$. To make up for it, I have now spelled out the first few cases explicitly, here