Timeline for Vietoris-Begle theorem for simplicial sets
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 16, 2015 at 15:38 | comment | added | Yonatan Harpaz | Sorry, then the fibers are not contractible. | |
| Oct 16, 2015 at 15:24 | comment | added | Yonatan Harpaz | Right. So take instead the map $B(\mathbb{Z}/2) \to \Delta^0$. | |
| Oct 15, 2015 at 21:54 | history | edited | Tom Goodwillie | CC BY-SA 3.0 |
added 195 characters in body
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| Oct 15, 2015 at 21:16 | comment | added | Omar Antolín-Camarena | The map $\Delta^0 \to B(\mathbb{Z}/2)$ is not surjective, which is one of the requirements in the question, @YonatanHarpaz. | |
| Oct 15, 2015 at 20:13 | comment | added | Yonatan Harpaz | Let $X$ be the nerve of the groupoid with one object and two automorphisms (also known as the classifying space of $\mathbb{Z}/2$). Then $X$ is a Kan complex with just one vertex but the corresponding map $\Delta^0 \to X$ does not induce an isomorphism on $H^1$ with coefficients in $\mathbb{Z}/2$ | |
| Oct 15, 2015 at 18:32 | comment | added | Ilias A. | in my version, X and Y are Kan complexes. Can you provide a counterexample? | |
| Oct 15, 2015 at 18:24 | history | answered | Tom Goodwillie | CC BY-SA 3.0 |