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Nov 25, 2010 at 9:52 comment added Jeffrey Giansiracusa yup. In fact, you can get an $E_\infty$ coalgebra structure on $C_*X$ and hence on $H_*X$, and an $E_\infty$ algebra structure on $C^*X$ and hence on $H^*(X)$ by transfer of structure (probably you need field coefficients, but not necessarily char zero).
Nov 25, 2010 at 6:50 history edited Romeo CC BY-SA 2.5
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Nov 25, 2010 at 6:34 comment added Kevin H. Lin I guess $C_\ast(X)$ has a dg coalgebra structure, and thus $H_\ast(X)$ has a "co-$A_\infty$" structure ... ?
Nov 25, 2010 at 2:01 history edited Romeo CC BY-SA 2.5
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Sep 28, 2010 at 9:36 vote accept Romeo
Sep 15, 2010 at 21:10 answer added Jeffrey Giansiracusa timeline score: 6
Sep 15, 2010 at 16:53 history asked Romeo CC BY-SA 2.5