Timeline for loop space of a finite CW-complex
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 4, 2020 at 21:13 | history | became hot network question | |||
| S Sep 4, 2020 at 16:18 | history | suggested | RobPratt |
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| Sep 4, 2020 at 16:02 | review | Suggested edits | |||
| S Sep 4, 2020 at 16:18 | |||||
| Sep 4, 2020 at 15:17 | vote | accept | cellular | ||
| Sep 4, 2020 at 14:28 | answer | added | Achim Krause | timeline score: 14 | |
| Sep 4, 2020 at 13:51 | comment | added | Ben Wieland | $H_0(\Omega X)$ is the free abelian group on $\pi_1(X)$. You might ask if that is the only problem; you might ask about the higher homology of the connected component of $\Omega X$: $\Omega_0X=\Omega \tilde X$, but this doesn't help. If you take any $X$ with infinite $\pi_1$ and glue on a sphere $S^n$ at a point, bad things happen. For example, $S^1\vee S^2$ has universal cover a line with infinitely many $S^2$ glued on, thus infinitely generated $H_2$; and so its loop space has infinitely generated $H_1$. | |
| Sep 4, 2020 at 13:35 | history | edited | cellular | CC BY-SA 4.0 |
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| Sep 4, 2020 at 13:32 | comment | added | Dylan Wilson | I guess if $X = S^1$ this is false, so definitely some $\pi_1$ conditions need to be made | |
| Sep 4, 2020 at 13:29 | history | edited | cellular | CC BY-SA 4.0 |
added 176 characters in body
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| Sep 4, 2020 at 13:16 | comment | added | Thomas Rot | I think the serre spectral sequence gives this immediately when X is simply connected | |
| Sep 4, 2020 at 13:13 | history | asked | cellular | CC BY-SA 4.0 |