Timeline for Intersection of subvector bundles
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 12, 2012 at 8:32 | vote | accept | Mirco | ||
| Jan 11, 2012 at 21:34 | comment | added | Liviu Nicolaescu | The smoothness comes form the representation of the projection as a contour integral. This integral depends smoothly on parameters. Note that in your problem you can assume from the very beginning that $E_1,E_2$ are defined on $B'=B_1\cap B_2$. Thus you can assume from the very beginning that $B=B_1=B_2$. Next, compactness is not needed. All we need is that for any compact $K$ the number $\inf_{b\in K}\lambda_b$ is positive. | |
| Jan 11, 2012 at 14:41 | comment | added | Mirco | I know that in the case of topological vector bundles the kernel of a vector bundle morphism is a vector bundle if the morphism is of constant rank. But I don't know if this holds in the smooth setting,too. I guess together with your beautiful diagonal construction, this will work, right? | |
| Jan 11, 2012 at 14:28 | comment | added | Mirco | nice answer. Unfortunately neither of $B$, $B_1$, $B_2$ nor $B_1 \cap B_2$ is assumed to be compact. | |
| Jan 11, 2012 at 13:38 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |