Timeline for Is the suspension of a weak equivalence again a weak equivalence?
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| May 13, 2015 at 2:12 | comment | added | Lennart Meier | You can view the unreduced suspension $\Sigma X$ as the homotopy pushout of $\ast \leftarrow X \rightarrow \ast$ - you can prove this and the statement you are interested in by the Theorem on p.80 in May's concise course on topology. | |
| May 13, 2015 at 1:35 | comment | added | user62675 | See Qiaochu Yuan's comment here: mathoverflow.net/questions/148963/… . Tyler Lawson says in an answer to that question that "[t]he unreduced suspension is more homotopically well-behaved, and in particular preserves weak equivalence because it only collapses along cofibrations". Not sure if this is what you wanted. | |
| May 13, 2015 at 1:07 | history | asked | Jens Reinhold | CC BY-SA 3.0 |