Timeline for Weak Vector Bundles
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 21, 2012 at 23:30 | vote | accept | John Klein | ||
| Jan 20, 2012 at 21:38 | answer | added | David Carchedi | timeline score: 8 | |
| Jan 20, 2012 at 20:19 | comment | added | John Klein | Yes, that's very convincing. It looks like my notion is only possibly interesting in the case non-locally compact spaces. But for my purposes, such spaces are pathological. So I guess I have a vector bundle after all! | |
| Jan 20, 2012 at 18:17 | comment | added | Apostolis Xekoukoulotakis | If we assume combatibility of structures, what martin says, and local compactness, then I think we can prove that it is a vector bundle. | |
| Jan 20, 2012 at 17:43 | comment | added | Chris Schommer-Pries | Being a vector bundle is a local structure, so if B is locally compact then E should just be a vector bundle in the usual sense, right? So am I right to surmise that you are concerned about a distinction that only exists for non-locally compact spaces? | |
| Jan 20, 2012 at 14:30 | history | edited | John Klein | CC BY-SA 3.0 |
added 102 characters in body
|
| Jan 20, 2012 at 14:28 | comment | added | John Klein | Martin: I hadn't considered that, but yes one should assume compatibility of structure under base change. | |
| Jan 20, 2012 at 5:51 | comment | added | Martin Brandenburg | It seems natural to require that each inclusion $K \subseteq K'$ yields a homomorphism of vector bundles $p|_K \to p|_{K'}$, right? | |
| Jan 19, 2012 at 22:32 | comment | added | Tom Goodwillie | By developing characteristic classes, I am guessing that you mean extending the usual classes to weak bundles (rather than, for example, developing obstructions for a weak bundle to be a bundle!). If so, then maybe you can pull back along a CW approximation of $B$ and get a bundle whose characteristic classes will give you singular cohomology classes of $B$. | |
| Jan 19, 2012 at 20:08 | comment | added | John Klein | I cannot make my example explicit to you since it's somewhat technical (it arises from stochastic dynamics). However, I do have a family of operators parametrized by a non-compact space (the space is a kind of configuration space). The groundstate (= null space) over each fiber is one dimensional and one can show that it gives a weak complex line bundle. I doubt that my example is an actual line bundle. | |
| Jan 19, 2012 at 17:59 | comment | added | Francesco Polizzi | Could you please provide an example of weak vector bundle which is not a vector bundle? | |
| Jan 19, 2012 at 17:22 | history | edited | John Klein | CC BY-SA 3.0 |
added 1 characters in body
|
| Jan 19, 2012 at 16:48 | history | asked | John Klein | CC BY-SA 3.0 |