Timeline for Geometry and Integrability in Other Bundles
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Oct 30, 2010 at 23:52 | comment | added | Deane Yang | Justin, in your question, you say "I can extend the above definition of involutive distribution to this subbundle in the obvious way. Let me take this as a definition of integrable subbundle." So aren't you claiming that you do have a definition of an involutive or integrable distribution for a vector bundle? | |
| Oct 30, 2010 at 22:22 | comment | added | Dick Palais | @Justin Curry: I don't believe so. Part of the reason is that it is not at all clear how to generalize the notion of integrability for an arbitrary vector bundle. (Actually, "worked out" is a somewhat misleading way of putting it: it makes it sound like there must be a natural generalization of those notions for subbundles of bundles more general than the tangent bundle, while what Deane Yang and I have been trying to say is that we do not believe this is so.) | |
| Oct 30, 2010 at 21:01 | comment | added | Justin Curry | Ah, part of my question was whether the notion of integrable or involutive had been worked out for arbitrary vector bundles. | |
| Oct 30, 2010 at 20:35 | comment | added | Deane Yang | In particular, it is not at all clear what "in the obvious way" means in the question. I suggest that the questioner try to work out the details of what "involutive" is supposed to mean for a vector bundle. As far as I know, there is no such concept. | |
| Oct 30, 2010 at 20:12 | history | answered | Dick Palais | CC BY-SA 2.5 |