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Timeline for transition in homotopy theory

Current License: CC BY-SA 4.0

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Mar 29, 2021 at 20:46 history edited Jeff Strom CC BY-SA 4.0
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Mar 28, 2021 at 15:57 comment added skupers By the way, mathoverflow.net/a/126841/798 gives detailed references for (2).
Mar 28, 2021 at 10:22 comment added Gael Meigniez Thank you, Denis and Maxime, for the pertinent answers (to a stupid question). Thank you, Skupers, for the reference to an author whom I should have known.
Mar 27, 2021 at 22:57 comment added skupers (2) As $\mathrm{Diff}(M)$ is a Frechet manifold, it is homotopy equivalent to a countable CW-complex and hence has countable homology groups. Look at the work of Michor.
Mar 27, 2021 at 22:28 comment added Maxime Ramzi No to 1- : take $X=Y=Z = S^1$, $f$ any index $2$ map and $g$ the identity (and here the obstruction is already at the group-theoretic level ! there are examples with "no group theoretic" obstructions but subtler homotopy theoretic obstructions)
Mar 27, 2021 at 22:28 comment added Denis Nardin (1) is very, very false. In general the problem of factorizing a map through another up to homotopy is attacked via obstruction theory and it's not trivial.
Mar 27, 2021 at 22:24 history asked Gael Meigniez CC BY-SA 4.0