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Mar 26, 2020 at 6:42 comment added Denis Nardin @GSM That's a fair point, but the $E_\infty$-structure itself is not very accessible (you can get the cup product structure, maybe the Dyer-Lashof action, but there's plenty of further structure there that is hard to read), so it hardly seems an improvement...
Mar 20, 2020 at 17:57 history edited Phil Tosteson CC BY-SA 4.0
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Mar 20, 2020 at 17:09 comment added GSM I see your point! The $C_{\ast}(Y)$ has more structure then just the structure of chain complex and the action of the fundamental group acts by preserving the structure of "$E_{\infty}$"-coring. Moreover, in my question I assume that we know more then just the homology, we know also the homotopy groups...
Mar 20, 2020 at 15:18 history edited Phil Tosteson CC BY-SA 4.0
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Mar 20, 2020 at 14:59 history answered Phil Tosteson CC BY-SA 4.0