Timeline for Does a compact semilocally simply connected geodesic space have the homotopy type of a CW complex?
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Aug 31, 2022 at 20:03 | answer | added | Cihan | timeline score: 3 | |
| Jan 12, 2011 at 19:42 | answer | added | Theo Buehler | timeline score: 9 | |
| Jan 12, 2011 at 19:04 | comment | added | Autumn Kent | @Bruno: Oops, nevermind, you're right. | |
| Jan 12, 2011 at 19:01 | comment | added | Autumn Kent | @Bruno, I think the cone over the Hawaiian earring is not geodesic, because there are points that are very close together (at height 1/2 in the cone) that are not joined by a short geodesic. (I could be wrong, I'm easily confused thinking about weird spaces.) | |
| Jan 12, 2011 at 18:56 | comment | added | Bruno Martelli | The cone over the Hawaiian earrings is semi-locally simply-connected and also geodesic, right? This space is not locally simply-connected. | |
| Jan 12, 2011 at 18:44 | comment | added | Autumn Kent | Do semilocally simply connected, geodesic, and compact imply that small balls are simply connected? The "counterexamples" I can think of aren't geodesic. If you have a locally finite cover by absolute retracts (ARs) with all intersections ARs, then Weil's theorem says the nerve is homotopy equivalent to the space. So maybe you could do a similar thing with a covering by simply-connected sets to get a compact nerve whose fundamental group surjects that of the space. (Local simple-connectivity would allow a map from the 2-skeleton of the nerve to the space.) | |
| Jan 12, 2011 at 17:38 | comment | added | Bruno Martelli | The Hawaiian earrings is not semi-locally simply-connected. | |
| Jan 12, 2011 at 16:25 | comment | added | Theo Buehler | I don't understand the comment in your edit: The fundamental group of the Hawaiian earrings is known to be uncountable, hence it cannot be finitely presented, at least as a discrete group. Could you clarify what you mean? | |
| Jan 12, 2011 at 13:37 | history | edited | Jim Conant | CC BY-SA 2.5 |
added 184 characters in body
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| Jan 12, 2011 at 13:35 | vote | accept | Jim Conant | ||
| Jan 12, 2011 at 13:33 | answer | added | Bruno Martelli | timeline score: 8 | |
| Jan 12, 2011 at 13:12 | history | asked | Jim Conant | CC BY-SA 2.5 |