Timeline for Homology of infinite intersection
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Dec 25, 2015 at 14:09 | history | edited | user9072 |
edited tags; edited tags
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| Apr 17, 2014 at 23:06 | comment | added | Włodzimierz Holsztyński | Let me make the above complete. Consider the category of h-pairs $\ (X\ A).\ $ These are pairs homotopically dominated (as pairs) by finite polyhedral pairs. Then this category admits exactly one E-S homology/cohomology theory (JK suggested to me to publish it in 1970/71). Here, in this topic, we still need to narrow the class of spaces to ANR-s to get answer YES because of the behavior of the inverse limit. | |
| Apr 17, 2014 at 22:52 | comment | added | Włodzimierz Holsztyński | Just in case, and for the sake of this topic, I'd like to stress quietly that when we talk about nice compact spaces, meaning ANR-s, then all E-S homology/cohomology theories are equivalent. | |
| Apr 17, 2014 at 22:46 | answer | added | Włodzimierz Holsztyński | timeline score: 0 | |
| Apr 17, 2014 at 22:16 | answer | added | Włodzimierz Holsztyński | timeline score: 1 | |
| Apr 17, 2014 at 20:43 | vote | accept | Peter Franek | ||
| Apr 17, 2014 at 16:32 | answer | added | jacob | timeline score: 3 | |
| Apr 17, 2014 at 16:26 | comment | added | Włodzimierz Holsztyński | It may be mentioned that here we talk about singular (?) homology, as opposed to Cech homology. | |
| Apr 17, 2014 at 15:58 | answer | added | HenrikRüping | timeline score: 1 | |
| Apr 17, 2014 at 12:42 | comment | added | Peter Franek | Thanks Jacob, maybe you are right, but now I'm not completely sure what you mean by "functorial map". Do you mean that H(\cap X_i) -> H(\cap Y_i) -> lim H(Y) equals H(\cap X_i) -> lim H(X) -> lim H(Y), i.e. Milnors surjective map is a natural transformation between the "H(\cap)" and the "lim H" functors? If yes, we don't see that at the moment. | |
| Apr 17, 2014 at 11:59 | comment | added | jacob | Perhaps I'm missing something subtle, but the map he defines is functorial, and is the inclusion-induced homomorphism for finite inverse limits. Thus, it is must also be the inclusion-induced homomorphism for infinite sequences (as you can see by truncating your sequence at fintie level). | |
| Apr 17, 2014 at 9:41 | history | asked | Peter Franek | CC BY-SA 3.0 |