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Jul 26, 2018 at 1:34 comment added John Klein @tictac I think you'll have to go back and dig up Bousfield's paper list as [5] in the paper I cited. Look at what I "added" in my answer. Judging from what Bousfield wrote, when $k =\Bbb Z/p$, $H_\ast(X;k)$ is trivial and $H^\ast(Y;k)$ is Hopf-like, it looks to me that in this case $H_\ast(F_\ast(X,Y);k)$ will be trivial when $X$ is $q$-dimensional and $Y$ is $(q-1)$-connected.
Jul 26, 2018 at 1:31 history edited John Klein CC BY-SA 4.0
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Jul 25, 2018 at 21:51 comment added tictac What can we say concretely in the case when $H_{\ast}(X;k)$ is trivial ?
Jul 25, 2018 at 21:45 history edited John Klein CC BY-SA 4.0
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Jul 25, 2018 at 21:39 history undeleted John Klein
Jul 25, 2018 at 21:39 history edited John Klein CC BY-SA 4.0
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Jul 25, 2018 at 21:36 history deleted John Klein via Vote
Jul 25, 2018 at 21:31 history answered John Klein CC BY-SA 4.0