Timeline for Automorphism groups and etale topological stacks
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| S Jan 28, 2018 at 22:00 | history | suggested | jeq | CC BY-SA 3.0 |
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| Jan 28, 2018 at 19:10 | review | Suggested edits | |||
| S Jan 28, 2018 at 22:00 | |||||
| May 9, 2011 at 13:39 | comment | added | David Carchedi | Thanks Andre. Is it easy to see that this is not coming from an etale groupoid? | |
| May 9, 2011 at 5:08 | comment | added | David Roberts♦ | Perhaps it is significant that the map Andre describes is a Dold Fibration that is not a Serre fibration (and hence not a Hurewicz fibration). And unless I'm mistaken, it's not even a local Serre fibration (in the sense that Noohi uses). | |
| May 8, 2011 at 23:00 | comment | added | Chris Schommer-Pries | Ooops! You're right. Okay, this also looks like a counter example to me. | |
| May 8, 2011 at 20:20 | comment | added | André Henriques | The two sets that you describe do not form a cover of $T$. You're missing the inverse image of {1}. | |
| May 8, 2011 at 20:09 | comment | added | Chris Schommer-Pries | Maybe I'm being dense. Doesn't any map f satisfy that property? Take $T_1$ to be the inverse image of the complement of [1,2], and likewise $T_2$ to be the inverse image of the complement of [0,1]? | |
| May 8, 2011 at 19:23 | comment | added | André Henriques | @Chris Schommer-Pries: Let $X$ be the above pushout stack. As you noted, there is a map from $X$ to $[0,2]$, but that map is not an isomorphism. For any topological space $T$, the induced map $\hom(T,X)\to \hom(T,[0,2])$ is injective, and the subset $\hom(T,X)\subset \hom(T,[0,2])$ can be characterized. A map $f:T\to [0,2]$ comes from a map $T\to X$ iff $T$ has an open cover $T=T_1\cup T_2$ such that $f(T_1)\subset [0,1]$ and $f(T_2)\subset [1,2]$. | |
| May 8, 2011 at 14:43 | comment | added | Chris Schommer-Pries | As a pushout, this stack admits a map to the space [0,2]. How exactly does it differ from this space? | |
| May 8, 2011 at 13:23 | history | edited | André Henriques | CC BY-SA 3.0 |
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| May 8, 2011 at 12:33 | history | edited | André Henriques | CC BY-SA 3.0 |
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| May 8, 2011 at 12:27 | history | answered | André Henriques | CC BY-SA 3.0 |