Timeline for Homotopy extension of $E_{\infty}$-spaces
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 8, 2020 at 2:27 | vote | accept | Paris | ||
| Jan 4, 2020 at 15:33 | answer | added | Peter May | timeline score: 19 | |
| Jan 4, 2020 at 9:47 | comment | added | Paris | @LennartMeier $X$ is connected, in particular grouplike. It was also my first guess... | |
| Jan 4, 2020 at 8:30 | comment | added | Lennart Meier | @DenisNardin Of course, right. I was not paying attention. | |
| Jan 4, 2020 at 7:30 | comment | added | Denis Nardin | @LennartMeier Unless I'm mistaken $B\Omega X$ is the connected component of the identity of $X$ (the group completion is $\Omega BX$) | |
| Jan 4, 2020 at 7:23 | comment | added | Lennart Meier | The second line of argument says that you are basically looking for $\Omega X$-principal bundles on $X$ and these should be classified by a map $X \to B \Omega X$. The latter is precisely the group completion of $X$ (for a modern reference see e.g. uni-muenster.de/IVV5WS/WebHop/user/nikolaus/papers/… ). For an "$E_{\infty}$-principal bundle" I expect $E_{\infty}$-maps. But this is just a guess. | |
| Jan 4, 2020 at 7:20 | comment | added | Lennart Meier | My guess is that it corresponds to homotopy classes of $E_{\infty}$-spaces from $X$ into the group completion of $X$. I have to sketches of an argument: First, if we also assume that $X$ is grouplike, then we can use that group-like $E_{\infty}$-spaces are the "same" as connective spectra and thus we are looking at (co)fiber sequences of spectra and can use that the homotopy category of spectra is triangulated. | |
| Jan 4, 2020 at 7:16 | history | edited | Lennart Meier | CC BY-SA 4.0 |
title corrected
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| Jan 3, 2020 at 23:46 | history | edited | Paris | CC BY-SA 4.0 |
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| Jan 3, 2020 at 22:57 | history | edited | Paris | CC BY-SA 4.0 |
added 58 characters in body
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| Jan 3, 2020 at 22:51 | history | asked | Paris | CC BY-SA 4.0 |