Timeline for A Problem about affine transformation
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 12, 2013 at 19:03 | comment | added | woodbass | @Rupert:Hi,Rupert. I have noticed you by email that I have proved your above statement but I haven't heard from you so far. I am drafting the proof. | |
| Jan 11, 2013 at 12:48 | comment | added | Rupert | I thank woodbass for pointing out the error in Theorem 3.1 of my thesis. I have been pondering these issues since he sent me that message, and I believe I have a modified statement which is true: namely, a map $RP^{n}\rightarrow RP^{n}$ preserving collineaity, whose image contains at least $n+2$ points any $n+1$ of which are in general position, is an element of $PGL(n,R)$. I hope to write up the proof of this soon. I also believe that I can answer the question originally posed in this thread in the affirmative. I will communicate with woodbass about this shortly. | |
| Jan 1, 2013 at 7:07 | comment | added | woodbass | In his proof, he actually made use of certain injectivity in some hyperplane because he thought that $f$ preserves parallelism which is not assumed in advance. Even if his "Theorem 3.1$ is true, we cannot deduce any definite answer to my problem. | |
| Jan 1, 2013 at 6:57 | comment | added | woodbass | There is an essential gap in his proof. I have written to him to point out the gap and he acknowledged his mistake. A simple counterexample to attack his "Theorem 3.1" is as follows (for simplicity let $n=2$). $f:RP^2\to RP^2$, let $f$ fix every point in some line $L$ and map the complement to one point outside $L$. | |
| Jan 1, 2013 at 5:29 | history | edited | Misha | CC BY-SA 3.0 |
added 25 characters in body
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| Dec 31, 2012 at 22:05 | history | answered | Misha | CC BY-SA 3.0 |