Timeline for Connective spectra and infinite loop spaces
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 14, 2017 at 20:01 | vote | accept | Matthias Ludewig | ||
| Sep 13, 2017 at 7:06 | answer | added | user43326 | timeline score: 4 | |
| Sep 12, 2017 at 20:22 | answer | added | Anton Fetisov | timeline score: 11 | |
| Sep 12, 2017 at 18:37 | history | edited | Matthias Ludewig | CC BY-SA 3.0 |
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| Sep 12, 2017 at 18:15 | comment | added | Matthias Ludewig | @Anton: Why would I require the delooping to be $(n-1)$-connected? I can surely take the $n$-fold loop space of a space that is not $(n-1)$-fold connected? Maybe this is the issue: If one makes this requirement, then one gets connective spectra, otherwise one gets any spectrum? | |
| Sep 12, 2017 at 17:07 | comment | added | Anton Fetisov | You've got your definition of an $\infty$-loop space wrong. An $\infty$-loop space is a space admitting all deloopings (strictly speaking, equipped with a specific choice of them). An n-fold delooping of an n-fold loop space is by definition an $(n-1)$-connected basepointed space, so in your sequence each $Y_i$ must be $(i-1)$-connected, unlike the case of general spectra. | |
| Sep 12, 2017 at 17:03 | comment | added | Phil Tosteson | Truncate $X_j$ to have no homotopy groups above degree $j$, and you get a connective spectrum with 0th space $Y_0$. The point is that there is a unique connective spectrum with $Y_0$ as it's zeroth space | |
| Sep 12, 2017 at 16:38 | history | asked | Matthias Ludewig | CC BY-SA 3.0 |