Timeline for Does the suspension spectrum functor preserve weak equivalences?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 16, 2020 at 9:13 | comment | added | nikola karabatic | @Tyrone if you write this as an answer I will accept it :) | |
| Jul 15, 2020 at 10:51 | comment | added | nikola karabatic | This sounds good, didn't know the computation about the n-dimensional HE | |
| Jul 15, 2020 at 10:09 | comment | added | Tyrone | What do you mean by acyclic here? If you don't want to use homology, then just use the computation of $\pi_n$ of the $n$-dimensional Hawaiian Earing (which the the $(n-1)$-fold reduced suspension of the Hawaiian Earing). | |
| Jul 15, 2020 at 9:57 | comment | added | nikola karabatic | Or did you intend to argue in another way? | |
| Jul 15, 2020 at 9:57 | comment | added | nikola karabatic | Hmm you are right about the homology, but I think this argument uses the suspension iso for reduced suspension and reduced homology implicitely and this does NOT hold for not-well-pointed spaces (since the reduced cone is not acyclic, at least I don't see why it should be). | |
| Jul 15, 2020 at 9:52 | comment | added | Tyrone | Enough of the homology of the Hawaiian earing is known and is not the homology of the wedge. In fact $\pi_n$ of the $n$-dimensional Hawaiian earing is known (and it is not even free abelian if I recall). | |
| Jul 15, 2020 at 9:45 | comment | added | nikola karabatic | @Tyrone: it is not clear to me whether the map becomes a weak equivalence after suspending further | |
| Jul 14, 2020 at 19:47 | comment | added | Tyrone | Doesn't your counterexample in $2$ answer this in the negative if $X,Y$ are not well-pointed? | |
| Jul 9, 2020 at 14:34 | history | asked | nikola karabatic | CC BY-SA 4.0 |