Timeline for Restriction function as a Morse function
Current License: CC BY-SA 4.0
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| Aug 4, 2021 at 3:07 | review | Close votes | |||
| Aug 8, 2021 at 2:34 | |||||
| Jul 25, 2021 at 4:31 | comment | added | Ryan Budney | Then I think the answer is yes. Step (1) perturb the surface to be disjoint from the critical points of $h$. Step (2) Use that $h$ is a submersion in a neighbourhood of the surface. Specifically, $h$ restricted to the surface may not be Morse, but a small perturbation of it is. Using the local triviality of $h$ near the surface allows you to perturb the surface, using the flow of a vector field, to mimic the perturbation of a non-Morse function to a Morse function. | |
| Jul 25, 2021 at 4:19 | history | edited | Zhiqiang | CC BY-SA 4.0 |
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| Jul 25, 2021 at 4:19 | comment | added | Zhiqiang | @RyanBudney I forgot to add that $h$ is a Morse function in $\mathbb R^3$. | |
| Jul 25, 2021 at 4:11 | review | Close votes | |||
| Jul 30, 2021 at 17:09 | |||||
| Jul 25, 2021 at 3:54 | comment | added | Ryan Budney | No, of course not. For example, what if $h$ is constant? | |
| Jul 25, 2021 at 3:51 | history | asked | Zhiqiang | CC BY-SA 4.0 |