Timeline for Higher Cerf Theory
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 4, 2014 at 12:36 | comment | added | Liviu Nicolaescu | I don't know. You have to check that book. I don't have it with me. | |
| Oct 3, 2014 at 15:02 | comment | added | Nerses Aramian | Could one say something to the effect, that for a function in the codimension n-stratum $f:M\rightarrow\mathbb{R}$, the critical points are isolated or that the preimages have measure 0? | |
| Oct 3, 2014 at 14:57 | vote | accept | Nerses Aramian | ||
| Oct 3, 2014 at 14:38 | comment | added | Liviu Nicolaescu | That is correct. $C^\infty(M)$ comes with a Whitney like stratification and essentially the question boils down to understanding the codimension $n$-strata and the lower codimension strata containing in their closure a given codimension $n$-stratum. This turns out to be very difficult. | |
| Oct 3, 2014 at 14:34 | comment | added | Nerses Aramian | Based on your response, my impression is that there is no general theory that works for arbitrary $n$. Is that right? | |
| Oct 3, 2014 at 9:19 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
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| Oct 3, 2014 at 9:03 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |