Timeline for p-local space vs p-completion
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 12, 2016 at 14:25 | history | edited | Sean Lawton | CC BY-SA 3.0 |
Formatting and grammar edits.
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| Sep 5, 2015 at 16:38 | answer | added | user62675 | timeline score: 2 | |
| Aug 24, 2015 at 8:37 | comment | added | user43326 | As to the second point, when $X$ is a circle, its $\pi _1$ acts nilpotently on all $\pi _i(X)$ since higher homotopy groups are trivial and the action on $pi _1$ is by identity, so localization and completion behave reasonably, but even in this case localization and completion differ. By localizing one gets $K(Z_{(p)},1)$, by completing one gets $K(Z_p^{\wedge },1)$. | |
| Aug 24, 2015 at 8:24 | comment | added | user43326 | On the first point, the p-localization localizes the homotopy groups whereas the p-completion completes the homotopy groups. So if all the higher homotopy groups are {\it finite} the completion and localization are same, but finitely generated doesn't suffice. For example take $K(Z,2)$. Localization gives $K(Z_{(p)},2)$ whereas the completion gives $K(Z_p^{\wedge},2)$. | |
| Aug 23, 2015 at 18:58 | history | undeleted | sphere | ||
| Aug 23, 2015 at 18:58 | history | deleted | sphere | via Vote | |
| Aug 23, 2015 at 18:51 | history | undeleted | sphere | ||
| Aug 23, 2015 at 18:46 | history | deleted | sphere | via Vote | |
| Aug 23, 2015 at 18:43 | history | asked | sphere | CC BY-SA 3.0 |