Timeline for Group Structure on CP^infinty
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 18, 2021 at 18:28 | comment | added | Daniel Asimov | S<sup>7</sup> does not support a homotopy-associative H-space structure. I.M. James proves (Trans. AMS, March 1957) in "Multiplication on Spheres (II)", Theorem 1.4: "There exists no homotopy-associative multiplication on S<sup>n</sup> unless n = 1 or 3." | |
| Jun 16, 2011 at 9:20 | answer | added | Grigory M | timeline score: 3 | |
| Jan 21, 2010 at 21:07 | vote | accept | Justin Curry | ||
| Jan 21, 2010 at 21:06 | vote | accept | Justin Curry | ||
| Jan 21, 2010 at 21:07 | |||||
| Jan 21, 2010 at 21:06 | vote | accept | Justin Curry | ||
| Jan 21, 2010 at 21:06 | |||||
| Jan 21, 2010 at 21:06 | vote | accept | Justin Curry | ||
| Jan 21, 2010 at 21:06 | |||||
| Jan 21, 2010 at 8:58 | answer | added | Oren Ben-Bassat | timeline score: 3 | |
| Jan 21, 2010 at 8:49 | answer | added | Andrew Stacey | timeline score: 13 | |
| Jan 21, 2010 at 4:02 | answer | added | algori | timeline score: 11 | |
| Jan 21, 2010 at 2:22 | comment | added | Jason DeVito - on hiatus | Thanks for the clarification! I wasn't sure about associativity (I'm not so sure why I DIDN'T think octonionic multiplication would give it an H-space structure - just shows I STILL have no intuition about the octonians!). | |
| Jan 21, 2010 at 1:53 | comment | added | Charles Siegel | $S^7$ does support an H-space structure. Give it as the unit octonians, the only thing that fails to hold exactly is associativity, but it holds up to homotopy. The spheres that admit H-space structures are precisely the unit vectors in a normed division algebra. It's a theorem of Adams that these are the only ones. | |
| Jan 21, 2010 at 1:12 | comment | added | Jason DeVito - on hiatus | For 3., see mathoverflow.net/questions/11117/… For 2, S^7 doesn't support a group structure. I don't THINK it supports an H-space structure either, but that I'm much less sure about. | |
| Jan 21, 2010 at 0:27 | history | asked | Justin Curry | CC BY-SA 2.5 |