Timeline for Embedding Euclidean buildings into products of trees
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 18, 2015 at 2:28 | vote | accept | user65993 | ||
| Jan 17, 2015 at 2:25 | answer | added | Misha | timeline score: 6 | |
| Jan 15, 2015 at 13:45 | comment | added | user65993 | Prof. de Cornulier: Thank you. So it appears that my slightly stronger question may be open as well (or false), but certainly that no proof is known. Do you know of a reference to read more about these specific examples? | |
| Jan 15, 2015 at 10:03 | comment | added | YCor | It's an open question whether $SL_{3}(\mathbf{Q}_p)$ (or equivalently its Euclidean building) has a quasi-isometric embedding into a product of trees (and more generally $SL_d(\mathbf{Q}_p)$ or $SL_d(\mathbf{R})$ for some/any $d\ge 3$). | |
| Jan 15, 2015 at 9:49 | comment | added | Alain Valette | You're right, I overlooked the surjectivity issue. I leave my comment however, as a very partial contribution. | |
| Jan 14, 2015 at 23:47 | history | edited | user65993 |
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| Jan 14, 2015 at 23:10 | comment | added | user65993 | Prof. Valette: Thank you for the response. I don't see how Theorem 1.1.2 in Kleiner-Leeb answers my question, as the quasi-isometries considered in that theorem are assumed to be (coarsely) surjective, whereas I am only interested in an embedding result. (Or did I misunderstand? I reiterate my lack of expertise re: buildings.) | |
| Jan 14, 2015 at 22:45 | comment | added | Alain Valette | I think taking $p=1$ is prevented by the Kleiner-Leeb result on quasi-isometric rigidity of Euclidean buildings: see Theorem 1.1.2 in math.nyu.edu/~bkleiner/symm.pdf | |
| Jan 14, 2015 at 21:04 | review | First posts | |||
| Jan 14, 2015 at 21:29 | |||||
| Jan 14, 2015 at 21:02 | history | asked | user65993 | CC BY-SA 3.0 |