Timeline for functions which covers(good covers) manifolds
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 3, 2014 at 21:41 | comment | added | Ali Taghavi | For a manifold $M$, we define the minimum $k$ such that a good covering of $M$ can be obtained via pull back of an open covering of $\mathbb{R}^{k}$ for some smooth function $f:M\to \mathbb{R}^{k}$. Is this invariant some how related to some thing as LS category as in the answer of @Eric? As you said this minimum is less than $2n+1$. Thanks again for your interesting answer. | |
| Nov 3, 2014 at 21:36 | comment | added | Ali Taghavi | @ToddTrimble Thanks for your very interesting answer. What about the following possible definition: | |
| Nov 3, 2014 at 5:58 | comment | added | Todd Trimble | @PaulSiegel I suspect you're right. I confess that when I wrote those words, I was in the midst of deploying greater nuclear power by first putting a Riemannian structure on $M$, and then using the Nash embedding theorem to isometrically embed in Euclidean space. Then it occurred to me that the above would involve much less weaponry. :-) | |
| Nov 3, 2014 at 4:28 | comment | added | Paul Siegel | I could be wrong, but I suspect this particular mosquito is genetically engineered to resist non-nuclear weaponry. In other words, I think the result is no easier than the Whitney embedding theorem. | |
| Nov 2, 2014 at 19:18 | history | answered | Todd Trimble | CC BY-SA 3.0 |