Timeline for Ends of Coxeter Groups
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 12, 2022 at 12:05 | comment | added | YCor | Note: My comment above is addressed by Thomas Weigel in these 2018 slides ("An Ihara-type theorem for buildings"), for the "Trees, dynamics and locally compact groups" conference in Düsseldorf, Germany, 29.6.2018. These slides include a screenshot of this MO page (with comments), and include "In particular, Y. Cornulier’s question has an affirmative answer." I don't know if the author has attempted to publish this result. | |
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
|
|
| Sep 10, 2014 at 18:22 | comment | added | Nick Gill | @YCor, of course your comment is entirely reasonable. There are plenty more results in the cited text that give more explicit information (see especially Thm. 8.7.3)... but I don't want to write them all out! | |
| Sep 10, 2014 at 17:46 | comment | added | YCor | Here are 1 source of multi-ended Coxeter group: when there is a partition $S=A\cup C\cup B$ with $A,B$ non-empty, such that all edges between $A$ and $B$ are labeled $\infty$, and such that the subgroup generated by $C$ is finite. This is something checkable. Maybe there are other obvious sources of multi-ended Coxeter groups, and it would be natural to wonder if they are the only ones. | |
| Sep 10, 2014 at 17:42 | comment | added | YCor | I would not consider this as a satisfactory answer, since it changes a problem into another one. I would consider as a full answer one describing in terms of the combinatorial data defining the Coxeter group. For instance just describing when the Coxeter group is finite involves a quite lengthy list. Describing when it has 2 ends is just, in the connected case, the case of the infinite dihedral group. (...) | |
| Sep 10, 2014 at 17:30 | vote | accept | Nicolas Boerger | ||
| Sep 10, 2014 at 17:22 | history | answered | Nick Gill | CC BY-SA 3.0 |