Timeline for Continuous orthogonal preserving maps between projective space
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 17, 2017 at 19:05 | comment | added | user43326 | @AliTaghavi if $n<m$, then the natural inclusion has the property stated in the question. | |
| Aug 16, 2017 at 17:56 | comment | added | Ali Taghavi | @NeilStrickland(and @Tsemo)) what can be said about the homotopy class of any such map when n=m). For n=m=1, the map can not be null homotopic but what about higher values of n=m). What can think to the same question for n<m. | |
| Aug 16, 2017 at 17:36 | vote | accept | Ali Taghavi | ||
| Aug 16, 2017 at 17:36 | comment | added | Ali Taghavi | @NeilStrickland (and @Tsemo) My apology for my bad and trivial question. it is fair that the question will be voted to closed. thanks for help of you. | |
| Aug 16, 2017 at 14:42 | comment | added | Neil Strickland | Or more directly: just choose $n+1$ mutually orthogonal lines in $\mathbb{C}^{n+1}$, and apply $f$ to obtain $n+1$ mutually orthogonal lines in $\mathbb{C}^{m+1}$, which is impossible. | |
| Aug 16, 2017 at 12:11 | comment | added | Tsemo Aristide | It is the image of $f$ restricted to the projective hyperplane $[H_x]$. | |
| Aug 16, 2017 at 12:08 | comment | added | Ali Taghavi | So what does it mean $f([H_x])$? f is defined on the projective space not on grassmanian. | |
| Aug 16, 2017 at 12:05 | comment | added | Tsemo Aristide | It is the orthogonal hyperplane to $x$. I fix an $x$, no need to choose $H_x$ continuously. | |
| Aug 16, 2017 at 11:35 | comment | added | Ali Taghavi | What is $H_x$? is it a line?How do you choose it, continuously? | |
| Aug 16, 2017 at 11:27 | history | answered | Tsemo Aristide | CC BY-SA 3.0 |