Timeline for simplicial structure on a flat fiber bundle
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Sep 25, 2017 at 12:17 | vote | accept | ort96 | ||
| Sep 24, 2017 at 8:41 | vote | accept | ort96 | ||
| Sep 24, 2017 at 8:51 | |||||
| Sep 20, 2017 at 3:14 | answer | added | Misha | timeline score: 1 | |
| Sep 19, 2017 at 19:38 | history | edited | ort96 | CC BY-SA 3.0 |
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| Sep 19, 2017 at 19:35 | comment | added | ort96 | Thanks. Yes, fiberwise homotopy equivalence is the correct notion for my problem. | |
| Sep 18, 2017 at 18:38 | comment | added | Dan Ramras | I think one would need to have specific goals in mind in order to really give an answer here. For instance, are you interested in fiber-wise homotopy equivalences? Are there some types of invariants you want to compute, for which you are hoping to replace a given bundle by something simplicial that will have the same invariants? | |
| Sep 17, 2017 at 18:25 | comment | added | Sebastian Goette | If you consider flat fibre bundles "as is", the action can be as ugly as you want. For example, take $B=S^1$, then the action is described by a single homeomorphism $\Phi$ of $F$. Try $F=S^1$ and let $\Phi$ be a rotation by an irrational multiple of $\pi$. Then $\Phi$ cannot be simplicial. Or are you allowed to consider actions up to isotopy or spaces as fibres up to some equivalence in your specific problem? | |
| Sep 15, 2017 at 22:30 | comment | added | ort96 | You are right, 'reasonable' was very vague. (edited the question a bit) I am trying to understand how much smaller the category of fiber bundles of form (ii) is versus those of form (i). Is there even a difference? Does that difference vanish if we look at those categories modulo homotopy equivalences? | |
| Sep 15, 2017 at 22:23 | history | edited | ort96 | CC BY-SA 3.0 |
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| Sep 15, 2017 at 3:22 | comment | added | Dan Ramras | I don't understand what is being asked, exactly. You've defined flat fiber bundles as twisted products, and then you ask if it's reasonable to assume something about the action of $\pi_1$. Adding hypotheses is quite often reasonable, if you can deduce something interesting from them. Without more information about your motivation, it seems impossible to say anything mathematical here. | |
| Sep 14, 2017 at 14:45 | review | First posts | |||
| Sep 14, 2017 at 14:45 | |||||
| Sep 14, 2017 at 14:42 | history | asked | ort96 | CC BY-SA 3.0 |