Timeline for Is there an analogue of CW-complexes built from $K(\mathbb Z, n)$ instead of $S^n$?
Current License: CC BY-SA 3.0
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| Dec 16, 2016 at 22:12 | vote | accept | evgeny | ||
| Dec 16, 2016 at 22:12 | answer | added | Dan Ramras | timeline score: 2 | |
| Dec 15, 2016 at 19:01 | comment | added | evgeny | @DanRamras, can you make your comment an answer, please, so that I could accept it? | |
| Nov 24, 2016 at 21:44 | history | edited | evgeny | CC BY-SA 3.0 |
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| Nov 24, 2016 at 21:34 | history | edited | evgeny | CC BY-SA 3.0 |
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| Nov 24, 2016 at 18:33 | comment | added | Dan Ramras | You may find Peter May's article "The Dual Whitehead Theorems" interesting in this context. It's at math.uchicago.edu/~may/PAPERS/47.pdf | |
| Nov 24, 2016 at 16:50 | comment | added | Denis Nardin | @evgeny It is still quite vague. At least to me a CW-complex is a kind of structure you put on a space to help computations. You can construct the category of Postnikov towers and it will be equivalent to the usual category of spaces (at least in a suitably weak sense). However it does not feel "dual" to the category of CW complexes in any meaningful sense. Is this the kind of answer you are after? | |
| Nov 24, 2016 at 16:33 | answer | added | David White | timeline score: 5 | |
| Nov 24, 2016 at 16:30 | history | edited | evgeny | CC BY-SA 3.0 |
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| Nov 24, 2016 at 16:25 | comment | added | evgeny | Najib, Denis, thank you, I modified the question. | |
| Nov 24, 2016 at 16:24 | history | edited | evgeny | CC BY-SA 3.0 |
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| Nov 24, 2016 at 16:13 | history | edited | evgeny | CC BY-SA 3.0 |
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| Nov 24, 2016 at 16:13 | comment | added | Denis Nardin | I am not sure I understand your question: in a "nice enough" category of spaces every space has a Postnikov tower (although saying that a Postnikov tower is "constructed" by Eilenberg-MacLane spaces might be overstating things). Can you elaborate on what kind of construction would you want? | |
| Nov 24, 2016 at 16:13 | comment | added | Najib Idrissi | Isn't $\Omega^{n-1} S^1$ the looping (and not delooping) of $S^1$? I believe the delooping would more traditionally be written as $B^{n-1}S^1$. | |
| Nov 24, 2016 at 16:10 | history | asked | evgeny | CC BY-SA 3.0 |