Timeline for When is the quotient by an $n$-fold loop space an $m$-fold loop space?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Sep 9, 2015 at 19:25 | comment | added | Jonathan Beardsley | @JesperGrodal okay, good. At least I'm not totally lost here... so I suppose my question is that a lot of times even the group theoretic quotient has such a universal property, and I'm wondering if it has any such thing here. | |
| Sep 9, 2015 at 19:17 | comment | added | Jesper Grodal | @JonBeardsley It all depends on what you mean by "reasonable" and what you mean by "quotient" ;) What is true is that if F -> E -> B is a principal fibration (like the sequence above) then F is equivalent to group which acts on E, and B can be identified with the Borel construction of the action of F on E. But what Amrani is saying is that this is not taking a cofiber, neither in spaces nor A_infty space. | |
| Sep 9, 2015 at 18:56 | comment | added | Jonathan Beardsley | It can't be thought of as a quotient in any reasonable sense? Is it at least true that homogeneous spaces coming from fibrations can be thought of as quotients? | |
| Sep 9, 2015 at 15:52 | history | answered | Ilias A. | CC BY-SA 3.0 |