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Dec 28, 2019 at 18:09 comment added YCor The Ollivier-Wise Rips machine produces hyperbolic groups with an infinite Property T subgroup and arbitrary f.p. quotient (hence possibly without Property T). These hyperbolic groups don't have Property PW, hence are not cubulable.
Dec 28, 2019 at 16:56 answer added HJRW timeline score: 6
Dec 27, 2019 at 15:13 vote accept Yaniv Shakhar
Dec 26, 2019 at 11:31 comment added YCor A weaker notion, "PW" is just acting properly on a CAT(0) cube complex (possibly infinite-dimensional). It's much weaker than cubulable, still not satisfied by all hyperbolic groups (see AGenevois's answer), while satisfied by many groups.
Dec 26, 2019 at 11:19 history edited Yaniv Shakhar CC BY-SA 4.0
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Dec 26, 2019 at 11:06 answer added AGenevois timeline score: 11
Dec 26, 2019 at 10:37 history asked Yaniv Shakhar CC BY-SA 4.0