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Apr 25, 2022 at 3:49 comment added M.Ramana @MarkGrant Thanks a lot for your comment and the link.
Apr 25, 2022 at 3:49 comment added M.Ramana @JohnRognes Thank you so much for the example. Is any condition on $P$ under which we have $Fd(A)<Fd(P)$?
Apr 24, 2022 at 19:38 comment added John Rognes No. $A = S^1$ is a retract of $P = S^1 \vee S^1$, this $P$ is not a retract up to homotopy of this $A$, and the `fundamental dimension' is $1$ for both $A$ and $P$.
Apr 24, 2022 at 17:09 comment added Mark Grant If there exists a finitely dominated space A whose finiteness obstruction is nontrivial, that would give a counter example.
Apr 24, 2022 at 17:07 comment added Mark Grant en.m.wikipedia.org/wiki/Wall%27s_finiteness_obstruction
Apr 24, 2022 at 14:45 history asked M.Ramana CC BY-SA 4.0