Timeline for Space of sections of a fibre bundle with non-compact base space
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 23 at 23:36 | history | edited | David Roberts♦ | CC BY-SA 4.0 |
Links and formatting
|
| Mar 26, 2013 at 18:26 | comment | added | Tobias Diez | Another enquiry regarding the dependence on the exhaustion and the metric in the non-compact case, as I do not see it. I suspect you are referring to the seminorms $p_{K, k}(f) = sup_{x \in K}(|\nabla^i f (m) |)$. Let $(K_n)$ and $(L_i)$ be two different exhaustions by compact sets. By a standard argument each $L_i$ can be absorbed by one $K_n$, $\L_i \subseteq K_n$. Than trivially $p_{L_i} \leq p_{K_n}$ and the topology is independent on the choice of exhaustion. Furthermore, the metric always gets evaluated over compact sets and so each choice of metric should give equivalent topologies. | |
| Jan 2, 2013 at 13:15 | history | edited | Peter Michor | CC BY-SA 3.0 |
added 544 characters in body
|
| Jan 2, 2013 at 13:06 | history | edited | Peter Michor | CC BY-SA 3.0 |
added 633 characters in body
|
| Jan 2, 2013 at 11:01 | vote | accept | Tobias Diez | ||
| Jan 2, 2013 at 10:52 | comment | added | Tobias Diez | Thank you for pointing out the dependence on the construction. Do you know any independence-results if I fix a (pseudo-)Riemannian metric (even Lorentzian manifold if necessary) on the base space and restrict to affine or vector bundles (to include the additive structure Andrew Stacey pointed out)? | |
| Jan 2, 2013 at 10:13 | vote | accept | Tobias Diez | ||
| Jan 2, 2013 at 11:01 | |||||
| Dec 17, 2012 at 8:03 | history | answered | Peter Michor | CC BY-SA 3.0 |