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Timeline for Left orderable linear groups

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Feb 16, 2020 at 17:39 comment added YCor My own conjecture would be that there exists a nontrivial left-orderable group with Property T. Some little evidence comes from this answer: left-orderable is compatible with some weak form of Property T. Also the evidence in the opposite direction is not convincing to me: arithmetic lattices were initially seen as prototypical examples of Property T groups, but they're only some very special (though important) examples. Same for local indicability, and subgroups of diffeomorphism groups, which are only very special instances of left-orderable groups.
Nov 16, 2011 at 22:16 comment added Alain Valette There is a folk conjecture that a discrete, torsion free group with Kazhdan's property (T), cannot be left orderable.
Nov 16, 2011 at 19:43 vote accept CommunityBot moved from User.Id=6976 by developer User.Id=69903
Nov 16, 2011 at 19:38 history answered Andy Putman CC BY-SA 3.0