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Feb 2, 2016 at 19:39 comment added Igor Rivin @EricS. See my answer. This is all that is known.
Feb 2, 2016 at 16:58 comment added Eric S. Are free planar actions of surface groups understood?
Feb 2, 2016 at 15:17 comment added Ian Agol Good point, I misread the question as faithful.
Feb 2, 2016 at 15:16 answer added Igor Rivin timeline score: 1
Feb 2, 2016 at 14:54 history edited Steven Frankel CC BY-SA 3.0
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Feb 2, 2016 at 14:53 comment added Steven Frankel @YCor: By homeomorphisms. For cocompactness, let's just say every point can be taken into some fixed compact set.
Feb 2, 2016 at 14:53 comment added YCor Steven, please specify if you require an action by homeomorphisms or preserving some further structure. Also, please define cocompact, whose meaning is clear if the action is proper but has several non-equivalent meanings otherwise (namely one can require, or not, that the quotient be Hausdorff).
Feb 2, 2016 at 14:51 history edited Steven Frankel CC BY-SA 3.0
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Feb 2, 2016 at 14:50 comment added YCor @IanAgol: no, left-orderable countable groups do not necessarily act freely continuously on the line. A group acting freely continuously on the line is abelian.
Feb 2, 2016 at 14:44 history edited Steven Frankel CC BY-SA 3.0
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Feb 2, 2016 at 14:38 history asked Steven Frankel CC BY-SA 3.0