Timeline for Shrinking and stretching of vector bundles
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 22, 2020 at 20:34 | history | edited | user111 | CC BY-SA 4.0 |
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| Mar 4, 2020 at 22:34 | comment | added | Dmitri Panov | Dan, yes, for example, a good metric would be such that each fiber $\mathbb R^n$ is isometric to an open half of a unite sphere (it is identified with $\mathbb R^n$ by the projection from its centre). Such a metric is good because convex subsets of $\mathbb R^n$ correspond to convex subsets of the half-sphere. | |
| Mar 4, 2020 at 20:32 | comment | added | Dan Petersen | Thanks! For completeness, I guess a natural way to ensure that this construction exhausts $U$ is to put a Riemannian metric on the total space of $E$ and then in step 1) note that we can make sure that each $B_x$ contains all vectors whose distance to the complement of $U$ is at least $1/n$. | |
| Mar 4, 2020 at 18:24 | history | edited | Dan Petersen | CC BY-SA 4.0 |
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| Mar 4, 2020 at 18:24 | vote | accept | Dan Petersen | ||
| Mar 4, 2020 at 18:12 | history | answered | Dmitri Panov | CC BY-SA 4.0 |