Timeline for Dold-Thom and infinite symmetric power of an $H$-space
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 10, 2022 at 16:18 | vote | accept | user127776 | ||
| Jul 10, 2022 at 13:23 | answer | added | Tom Goodwillie | timeline score: 2 | |
| Jul 10, 2022 at 0:37 | history | edited | user127776 | CC BY-SA 4.0 |
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| Jul 9, 2022 at 19:06 | comment | added | Tom Goodwillie | Let's specify that the equivalence from $Sym^\infty(\mathbb P^\infty)$ to the product of the $K(2i,\mathbb Z)$ should be an $H$-space map, so that it is determined by its restriction to $\mathbb P^\infty$. And let's specify that the map $\mathbb P^\infty\to K(2i,\mathbb Z)$ should be the one that corresponds to the usual generator of $H^{2i}(\mathbb P^\infty)$. (There might be a sign ambiguity here, but I guess we know what we mean by the usual one.) In that case, I withdraw my objection. | |
| Jul 9, 2022 at 17:55 | comment | added | user127776 | But doesn't it change the morphism up to the automorphisms of the cohomology groups and automorphisms respect the cup product. What you are saying is like saying different models for Eilenberg Maclane spaces induce different cup products. | |
| Jul 9, 2022 at 17:38 | comment | added | Tom Goodwillie | Yes, it definitely does. | |
| Jul 9, 2022 at 0:34 | comment | added | user127776 | @TomGoodwillie Does choosing different homotopy equivalences lead to different maps on homotopy groups? I don't know an explicit homotopy equivalence but it is in the Dold-Thom paper. | |
| Jul 8, 2022 at 23:27 | comment | added | Tom Goodwillie | To have a definite question one must specify a particular homotopy equivalence to the product of $K(2i,\mathbb Z)$. | |
| Jul 8, 2022 at 20:29 | history | asked | user127776 | CC BY-SA 4.0 |