Timeline for Are $CAT(0)$-polygonal complexes median spaces?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2018 at 12:17 | answer | added | AGenevois | timeline score: 2 | |
| Oct 9, 2018 at 10:46 | history | edited | user129863 | CC BY-SA 4.0 |
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| Oct 9, 2018 at 7:45 | review | Close votes | |||
| Oct 14, 2018 at 3:05 | |||||
| Oct 9, 2018 at 6:50 | comment | added | AGenevois | @user129863: Your edited question is not clear either. What are the restrictions you impose on your new metric? Has it to induce the same topology? Has it to be Lipschitz equivalent or quasi-isometric to the previous metric? Because if you impose no restriction, just transfer a median metric through a bijection with a median space having the same cardinality. | |
| Oct 8, 2018 at 23:17 | history | edited | user129863 | CC BY-SA 4.0 |
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| Oct 8, 2018 at 16:25 | comment | added | AGenevois | Another remark is that real trees are the only examples of geodesic metric spaces which are both median and CAT(0). It follows from the fact that CAT(0) spaces are uniquely geodesic. | |
| Oct 8, 2018 at 13:49 | comment | added | YCor | The question is unclear if you don't specify the metric on the polygons. Beware that a CAT(0) cube complex of dimension $\ge 2$, with Euclidean cubes, is not a median space; when endowed with the $\ell^1$-metric on cubes, it is median but not CAT(0)! | |
| Oct 8, 2018 at 13:20 | review | First posts | |||
| Oct 8, 2018 at 13:42 | |||||
| Oct 8, 2018 at 13:17 | history | asked | user129863 | CC BY-SA 4.0 |