Timeline for Disturbing regular level submanifold of a smooth function
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 18, 2015 at 12:50 | comment | added | Gauss | @AlexDegtyarev, thank you. So, if I want to study zero set of some smooth function which is regular I can proceed as follows: approximate it wih Morse and study its topology. Very usefull thing then. | |
| Jan 18, 2015 at 12:27 | comment | added | Pietro Majer | A simple example: a smooth function on S^1xS^1 may have only 3 critical point, but if they are only 3 at least one is degenerate . | |
| Jan 18, 2015 at 12:25 | comment | added | Alex Degtyarev | In other words, you can always find a Morsification whose critical values are in arbitrary small n/hoods of those of the original function. Outside of those n/hoods, nothing happens: everything is locally trivial. | |
| Jan 18, 2015 at 12:23 | comment | added | Alex Degtyarev | Yes, of course. Morse functions constitute a dense subset. Although, of course, it is not true that there is a single Morsification not affecting any of the regular values: some will be affected (a singular point will break into several Morse ones). But you can always keep one favorite regular value. | |
| Jan 18, 2015 at 12:14 | comment | added | Gauss | @AlexDegtyarev, you mean that morsifications of a singular points can be provided in a sufficiently small neighbourhoods and this doesn't effect the regualr submanifolds? | |
| Jan 18, 2015 at 12:12 | comment | added | Gauss | @JoonasIlmavirta, I am interested in a topological difference, homology or something. especcialy in a low-dimensional cases 1,2 and 3. | |
| Jan 18, 2015 at 12:09 | comment | added | Alex Degtyarev | Different in what sense? They are certainly diffeomorphic as submanifolds (assuming, of course, that $a$ remains a regular value all the way during the perturbation); actually, they are even diffeotopic. As long as you are speaking about regular values, you do not need to bother about other singularities. | |
| Jan 18, 2015 at 12:08 | comment | added | Joonas Ilmavirta | How do you want to measure the difference of the two submanifolds? Hausdorff distance or something else? | |
| Jan 18, 2015 at 12:02 | review | First posts | |||
| Jan 18, 2015 at 12:09 | |||||
| Jan 18, 2015 at 12:02 | history | asked | Gauss | CC BY-SA 3.0 |