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Nov 26, 2023 at 18:37 comment added YCor This is called "Property PW" in some papers. I studied/surveyed it here.
Nov 26, 2023 at 13:55 comment added Matt Zaremsky Worth mentioning one little fact where the complex need not be finite dimensional: If a group acts properly on a CAT(0) cube complex then the group has the Haagerup property. This is the main thing I'm aware of that "still works" without finite dimensionality.
Nov 26, 2023 at 4:59 history became hot network question
Nov 25, 2023 at 23:20 comment added bishop1989 Thanks for both the answers! I didn't know that they are finitely generated.
Nov 25, 2023 at 22:21 answer added AGenevois timeline score: 12
Nov 25, 2023 at 22:06 comment added Matt Zaremsky Eh? $T$ and $V$ are in fact finitely generated (and finitely presented, and type $F_\infty$). I think they are a perfect example of the sort of thing you're asking about.
Nov 25, 2023 at 20:58 history asked bishop1989 CC BY-SA 4.0