Timeline for Delooping a fibration sequence with loopspace fiber and finite CW complexes
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2019 at 18:31 | answer | added | Mark Grant | timeline score: 6 | |
| Oct 23, 2019 at 18:01 | history | edited | Qayum Khan | CC BY-SA 4.0 |
EDIT: As suggested, I renamed the base space $B$ to $T$, in order to not confuse it with the classifying space functor. Also, I added two citations.
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| Oct 23, 2019 at 17:30 | history | edited | Qayum Khan | CC BY-SA 4.0 |
EDIT: As suggested, I renamed the base space $B$ to $T$, in order to not confuse it with the classifying space functor.
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| Oct 23, 2019 at 16:55 | comment | added | Denis T | @QayumKhan DenisNardin is right, I mean just an application of classifying space functor to map $\Omega T \to Aut(\Omega T)$ representing left (more precisely, the side $\pi_1$ of base acts on fiber in your preferrable conventions) multiplication. Also possibly you want to use Moore loops for that to avoid some nuances with non-strictly associative actions etc. | |
| Oct 23, 2019 at 7:48 | comment | added | Denis Nardin | @QayumKhan The tautological action is the one corresponding to the pathspace fibration $\Omega T\to P T\to T$ (morally it is the action of $\Omega T$ on itself by left(?) multiplication) | |
| Oct 22, 2019 at 23:32 | history | edited | Josiah Park | CC BY-SA 4.0 |
reverting title edit (was unfamiliar with word 'delooping' initially, my apologies)
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| Oct 22, 2019 at 23:16 | history | edited | Josiah Park | CC BY-SA 4.0 |
edited title
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| Oct 22, 2019 at 22:49 | comment | added | Qayum Khan | @Denis T. : Любезно, what is the explicit formula for this tautological action? Does it it assume that $T$ is a topological group, say by pointwise-conjugating a loop by an element of $T$? If so, isn't this instead a map $T \longrightarrow Aut(\Omega T)$? | |
| Oct 22, 2019 at 21:50 | comment | added | Denis T | (I rename $B$ to $T$ to avoid confusion) I think the only obstruction is factorizing action map $E \to BAut(\Omega T)$ through delooping of tautological action $T \to BAut(\Omega T)$ which is done by usual obstruction theory. | |
| Oct 22, 2019 at 20:49 | history | asked | Qayum Khan | CC BY-SA 4.0 |