Timeline for Cohomology of the interior of a zero set of a smooth function
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 25, 2011 at 16:04 | comment | added | David Carchedi | @Vitali: This question is a bit vague on purpose. Essentially, if there happens to be a way to compute the cohomology of the interior of the zero set of each smooth function on R^n, then this would give a way of computing the cohomology of $B\Gamma^n$. | |
| Nov 24, 2011 at 21:26 | comment | added | Vitali Kapovitch | the question is a bit too vague. of course a strong condition on f will say something about level and sublevel sets. e.g. if f is convex then the sublevel sets are convex and hence contractible. what do you really know about f in your situation? personally, I have used a variation of the above when f is partially k-convex which implied that sublevel sets have homotopy types of k-dimensional CW-complexes. | |
| Nov 17, 2011 at 20:07 | answer | added | Tara Holm | timeline score: 3 | |
| Nov 16, 2011 at 22:15 | comment | added | David Carchedi | Thanks Otis, but in fact I'm aware of this. See my comment to the answer of algori. | |
| Nov 16, 2011 at 18:58 | answer | added | algori | timeline score: 1 | |
| Nov 16, 2011 at 18:57 | comment | added | Otis Chodosh | Keep in mind that all closed sets are the zero set of a smooth function. | |
| Nov 16, 2011 at 17:03 | history | asked | David Carchedi | CC BY-SA 3.0 |