Timeline for Rational homology of $\Omega^2 ( \mathbb CP^n \vee S^d)$

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Feb 3, 2021 at 17:26	vote	accept	qqqqqqw
Feb 2, 2021 at 4:16	comment	added	user51223		Thanks to this great answer. I just like to add that a general result of Gray, generalising Hilton-Milnor decomposition, seems to be applicable to the above question. A first application describes $\Omega(\mathbb{C}P^n\vee S^{d})$ and then from his result one can get something for the double loop space. Indeed, a very useful assumption, perhaps implicit, is that $d>0$ so one can apply refined version of Gray's result (see the comments after Theorem). The paper I refer to is titled ``A note on the Hilton–Milnor Theorem''.
Jan 30, 2021 at 10:19	history	edited	Gregory Arone	CC BY-SA 4.0	added 468 characters in body
Jan 30, 2021 at 9:59	history	edited	Gregory Arone	CC BY-SA 4.0	added 79 characters in body
Jan 30, 2021 at 9:53	history	edited	Gregory Arone	CC BY-SA 4.0	added 46 characters in body
Jan 30, 2021 at 9:46	history	answered	Gregory Arone	CC BY-SA 4.0