Timeline for What does "higher monodromy" tell us about a principal bundle
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 2, 2015 at 0:28 | comment | added | Gustavo Granja | No problem. Regarding the homotopy lifting property, etc, I would recommend Husemoller - "Fibre bundles". Steenrod's book, "The Topology of Fibre bundles" is even better but it is a bit old fashioned. I am afraid I don't know a reference for the $A_\infty$ stuff. My first guess would be May's "Classifying spaces and fibrations" (available on his webpage) but a cursory search doesn't confirm my guess... I will try to look for a reference. | |
| Dec 2, 2015 at 0:10 | comment | added | Saal Hardali | This is exactly what I wanted thanks.The part with $Aut(P)$ was me incorrectly involving the global gauge group in the discussion. Thanks! Where would you recommend to read about all this homotopical algebraic perspective on fibre bundles? | |
| Dec 2, 2015 at 0:05 | comment | added | Gustavo Granja | I am a bit confused by your $Aut(P)$. I think the holonomy representation will just be a homomorphism $\phi \colon \Omega X \to G$. Then the answer to your question is that $\phi$ is homotopic to $\Omega f$ (in fact homotopic as an $A_\infty$ map). | |
| Dec 1, 2015 at 22:09 | vote | accept | Saal Hardali | ||
| Dec 1, 2015 at 21:43 | comment | added | Saal Hardali | whis was very helpful, thanks. One thing still bugs me though. Suppose I choose a connection for the bundle classified by $f$. This connection gives a holonomy representation $\Omega X \to Aut(P) \subset G$ into the gauge group of the bundle. What's the relation, if there's any at all, between this map and map $\Omega f : \Omega X \to G$? (I know the second map is unique only upto homotopy but stil...) | |
| Dec 1, 2015 at 15:03 | history | answered | Gustavo Granja | CC BY-SA 3.0 |