Timeline for Morse Theory and Exotic Spheres
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 2, 2012 at 13:35 | comment | added | Liviu Nicolaescu | @ Greg: In Milnor's Collected Papers, vol. 3 there is an introductory section entitled "How these papers came to be written" where he outlines the thought process that led him to the exotic spheres. It may not completely answer your question, but it is a nice window into his thinking. | |
| Oct 21, 2010 at 6:04 | vote | accept | Juan OS | ||
| Oct 21, 2010 at 6:04 | comment | added | Juan OS | In fact, if $h+j \neq \pm 1$ then the total space is not homeomorphic to the sphere, so the Morse function cannot have only two critical points! Thanks again! | |
| Oct 21, 2010 at 5:59 | comment | added | Juan OS | Thanks Greg, I realized this a couple of hours ago, conjugation is the key to it all, however, the Morse function doesnt piece together in quite the same way for all bundles, the fact that $h+j=1$ is crucial for in order for the function to be well defined, since otherwise the real part of $v$ would not be preserved! | |
| Oct 20, 2010 at 20:00 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |