Timeline for Closed free subgroups of the automorphism group of the countable atomless boolean algebra
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 31, 2018 at 10:34 | comment | added | YCor | (PS if $K$ is a local (locally compact) field of finite characteristic then it still works: $Aut(K)$ is (infinite) compact rather than finite, but this still proves closedness; Uri's answer shows that this could be deduced automatically by the way.) | |
| May 31, 2018 at 8:51 | history | edited | YCor | CC BY-SA 4.0 |
added Schottky example
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| May 29, 2018 at 22:32 | comment | added | YCor | For $d=2$ it's the stabilizer of the cross-ratio, hence it's closed. For $d\ge 3$ the stabilizer of the alignment relation is closed, and equal (fundamental theorem of projective geometry) to $PGL_d(K)\rtimes Aut(K)$ where Aut means topological field automorphisms, so its open subgroup of finite index $PGL_d(K)$ is closed as well. | |
| May 29, 2018 at 21:11 | vote | accept | Iian Smythe | ||
| May 29, 2018 at 20:01 | comment | added | Iian Smythe | Can you say a word about why these copies of $PGL_d(K)$ are closed in the group? | |
| May 29, 2018 at 18:42 | history | answered | YCor | CC BY-SA 4.0 |