Timeline for Examples of Morse functions on unit tangent bundle of the sphere $T^1(S^2)$
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 20, 2017 at 14:02 | answer | added | Pietro Majer | timeline score: 5 | |
| Oct 18, 2017 at 22:07 | history | edited | john mangual | CC BY-SA 3.0 |
added 154 characters in body
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| Oct 18, 2017 at 21:35 | comment | added | Ryan Budney | Most linear functions will be Morse. Given that the unit tangent bundle is quadratic, this is a very reasonable Morse-theory setup. | |
| Oct 18, 2017 at 20:19 | comment | added | john mangual | Even for reasonable choice of a section, a straightforward computation of the critical points could go awry. A natural-looking function might might be Morse due to a technicality. Non-generic behavior or the level sets is to be expected. | |
| Oct 18, 2017 at 19:55 | comment | added | Pietro Majer | Isn't $x_1+2v_2$ a Morse function? I haven't done the computation, but I'd say it has exactly $4$ critical points, namely $(\pm1,0,0;0,\pm1,0)$, of index $0,1,2,3$ | |
| Oct 18, 2017 at 19:11 | comment | added | მამუკა ჯიბლაძე | You are right, it is $SO(3)$ | |
| Oct 18, 2017 at 18:45 | comment | added | john mangual | @მამუკაჯიბლაძე $\mathbb{R}P^3$ ? | |
| Oct 18, 2017 at 18:36 | comment | added | მამუკა ჯიბლაძე | Is not this just $S^3$? | |
| Oct 18, 2017 at 18:06 | history | edited | john mangual | CC BY-SA 3.0 |
one more equation
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| Oct 18, 2017 at 17:52 | history | asked | john mangual | CC BY-SA 3.0 |