Timeline for If $\Omega X \simeq \Omega Y$ then is $X \simeq Y$ for $X,Y$ simply connected?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 22, 2019 at 13:58 | vote | accept | WhoAmI | ||
| Nov 22, 2019 at 13:26 | answer | added | Achim Krause | timeline score: 37 | |
| Nov 22, 2019 at 13:15 | review | First posts | |||
| Nov 22, 2019 at 13:48 | |||||
| Nov 22, 2019 at 13:14 | comment | added | Achim Krause | As written, this is false. What follows from Whitehead is that given a map $f: X\to Y$ between connected spaces, which induces an equivalence on loop spaces, it was an equivalence to begin with. This follows for example also from the fact that loop space and the bar construction constitute inverse equivalences between connected spaces and grouplike $\mathbb{E} _1$-spaces. | |
| Nov 22, 2019 at 13:10 | history | asked | WhoAmI | CC BY-SA 4.0 |