Timeline for Delooping maps between H-spaces
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Aug 12, 2011 at 11:58 | vote | accept | Ulrich Pennig | ||
| Jul 26, 2011 at 14:46 | answer | added | Oscar Randal-Williams | timeline score: 10 | |
| Jul 26, 2011 at 14:38 | comment | added | Torsten Ekedahl | You still have the same problem though in a slightly different form: A map on classifying spaces induces an $A_\infty$-map on the spaces and vice versa). Your condition even with both $G$ and $H$ being CW-complexes is weaker than that it only says that the map respects the products up to homotopy not up to higher homotopies which is what is required to be an $A_\infty$-map. | |
| Jul 26, 2011 at 12:42 | comment | added | Ulrich Pennig | changed $H$-space to $A_{\infty}$-space according to Torsten's comment | |
| Jul 26, 2011 at 12:41 | history | edited | Ulrich Pennig | CC BY-SA 3.0 |
changed to Ainfty-spaces
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| Jul 26, 2011 at 9:46 | comment | added | Torsten Ekedahl | It should have a given $A_\infty$-structure. Note that the actual choice of structure affects what the classifying space would be so you must specify it. A $\Gamma$-structure is stronger but again the choice of $\Gamma$-structure will affect what classifying space you are talking about. | |
| Jul 26, 2011 at 9:10 | comment | added | Ulrich Pennig | @Scott: Thank you. I corrected this. @Torsten: Hmm, in the case I have in mind, H is actually a Gamma-space, so it should have a classifying space. What are the conditions for an H-space to have a classifying space? | |
| Jul 26, 2011 at 9:08 | history | edited | Ulrich Pennig | CC BY-SA 3.0 |
added "iso of groups"
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| Jul 26, 2011 at 8:58 | comment | added | S. Carnahan♦ | I think you should emphasize that the isomorphism $[X, G] \to [X, H]$ is an isomorphism of groups, not just sets. This then yields the condition that $\pi_0(H)$ is a group and that $H$ has a classifying space. | |
| Jul 26, 2011 at 8:44 | comment | added | Torsten Ekedahl | $H$-spaces may not have classifying spaces. | |
| Jul 26, 2011 at 8:30 | history | asked | Ulrich Pennig | CC BY-SA 3.0 |