Timeline for Principal bundles that can't be detected by spheres
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 30, 2015 at 4:25 | comment | added | Robert Bruner | @Saal: Exactly: the induced map in homotopy is just the 0th layer of information contained in the map. Next one has Toda brackets (secondary compositions), tertiary, etcetera. | |
| Dec 29, 2015 at 23:57 | comment | added | Qiaochu Yuan | See mathoverflow.net/questions/2672/whitehead-for-maps for some discussion of "Whitehead's theorem for maps." | |
| Dec 29, 2015 at 23:51 | comment | added | Qiaochu Yuan | @Saal: yes, "Whitehead's theorem for maps" fails in a pretty serious way. It's possible to describe an obstruction theory for a map to be nullhomotopic but it's more complicated than looking at the induced map on homotopy groups. | |
| Dec 29, 2015 at 23:48 | comment | added | Saal Hardali | I have now a new appreciation for Whitehead's theorem | |
| Dec 29, 2015 at 23:41 | vote | accept | Saal Hardali | ||
| Dec 29, 2015 at 23:41 | comment | added | Saal Hardali | Thanks! This was very clear and interesting! So, one moral of this story would be that the action of a map on homotopy groups hardly tells you anything about it (which is not so hard to accept but I didn't really have this piece of intuition before). Thanks again! | |
| Dec 29, 2015 at 22:59 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Dec 29, 2015 at 22:50 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Dec 29, 2015 at 22:44 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Dec 29, 2015 at 22:38 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Dec 29, 2015 at 22:30 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
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| Dec 29, 2015 at 22:25 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |