Timeline for On Wilson's claim that Lyapunov function level sets are not exotic spheres
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 16, 2021 at 7:01 | comment | added | Gael Meigniez | I don't understand Byrnes' claims and arguments, and especially not on line 10 of page 341. Again, Freedman's beautiful result is topological, and implies no diffeomorphism between the level set and the 4-sphere, only a homeomorphism. | |
| Feb 14, 2021 at 22:30 | comment | added | Matthew Kvalheim | Regarding the case $n=5$ being open: I just discovered that, in the 2008 paper "On Brockett's Necessary Condition for Stabilizability and the Topology of Liapunov Functions on $\Bbb{R}^n$" by C. I. Byrnes, it seems to be claimed in his Theorem 3.1 that diffeomorphism holds even for $n=5$. (See also his Theorem 4.1 and Lemma 4.2 for similar claims). Based on what I have learned from your answers here, I am suspicious of what Byrnes claims. Do you think Byrnes is mistaken? | |
| May 24, 2017 at 20:08 | comment | added | Matthew Kvalheim | Many thanks for your answer. It's quite a coincidence to receive an answer from you since I currently happen to be reading your paper "Submersions, Fibrations, and Bundles." | |
| May 24, 2017 at 20:04 | vote | accept | Matthew Kvalheim | ||
| Jun 4, 2017 at 5:00 | |||||
| May 24, 2017 at 18:15 | history | answered | Gael Meigniez | CC BY-SA 3.0 |