Timeline for Is a simply connected elliptic space rationally homotopy equivalent to a loop space or a suspension?
Current License: CC BY-SA 3.0
7 events
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| Oct 31, 2017 at 0:42 | history | edited | Michael Albanese | CC BY-SA 3.0 |
deleted 15 characters in body; edited tags; edited title
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| Oct 31, 2017 at 0:31 | comment | added | tarik | my question about loop space is equivalent to when the rational cohomology algebra of X is a free graded commutative algebra. | |
| Oct 31, 2017 at 0:30 | answer | added | Aleksandar Milivojević | timeline score: 8 | |
| Oct 31, 2017 at 0:19 | comment | added | tarik | that's right but it can exist | |
| Oct 31, 2017 at 0:12 | comment | added | Arun Debray | Cup products on a suspension vanish. Given that elliptic simply connected spaces satisfy Poincaré duality over $\mathbb Q$, that severely limits your options for being rationally equivalent to a suspension. | |
| Oct 31, 2017 at 0:11 | comment | added | Qiaochu Yuan | $\mathbb{CP}^2$ is elliptic, it's definitely not a rational suspension, and I think it's not a rational loop space. | |
| Oct 30, 2017 at 23:35 | history | asked | tarik | CC BY-SA 3.0 |