Timeline for A Manifold for which $\chi^{\infty}(M)$ is rich
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| May 11, 2015 at 18:44 | comment | added | Robert Bryant | @AliTaghavi: The answer is essentially the same. In fact, I now see that I essentially gave the proof in the answer. I had forgot that. | |
| May 11, 2015 at 18:42 | comment | added | Ali Taghavi | Is the reason somehow similar to your answer to the main question of this post?If not, can you give a reference, please? | |
| May 11, 2015 at 18:39 | comment | added | Robert Bryant | @AliTaghavi: No, there is not. By a theorem of Cartan, $\mathrm{SL}(n{+}2,\mathbb{R})$ cannot act nontrivially on any manifold of dimension less than $n{+}1$. | |
| May 11, 2015 at 18:12 | comment | added | Ali Taghavi | Is there a nontrivial right action of $SL(n+2,\mathbb{R})$ on $\mathbb{R}^{n}$ or $S^{n}$? According to your answer, such actions can not be effective. So it would be interesting to find an element $g\neq e$ which fixss all elements. | |
| Mar 21, 2014 at 23:43 | review | Suggested edits | |||
| Mar 22, 2014 at 0:13 | |||||
| Mar 15, 2014 at 22:10 | vote | accept | Ali Taghavi | ||
| Mar 15, 2014 at 22:10 | comment | added | Ali Taghavi | Prof. Bryant, My deep thanks and respect to you for your help and very interesting answer. | |
| Mar 15, 2014 at 20:31 | history | edited | Robert Bryant | CC BY-SA 3.0 |
added some explanation and examples at the request of the OP
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| Mar 15, 2014 at 20:06 | comment | added | Robert Bryant | I'll add the explanations in the answer above. | |
| Mar 15, 2014 at 19:54 | comment | added | Ali Taghavi | Prof. Bryant Thank you very much for your answer. May I ask you that you more explain?: Why it does not work for $M=\mathbb{R}$? as you started from $\mathbb{R}^{2}$. What is the reason for $\mathbb{R}^{2}$?Is this situation possible for a compact manifold for example spheres? | |
| Mar 15, 2014 at 15:44 | history | edited | Robert Bryant | CC BY-SA 3.0 |
added some information
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| Mar 15, 2014 at 14:20 | history | answered | Robert Bryant | CC BY-SA 3.0 |